Claims

Claim Status Table

Claims are organized by epistemic layer. Failure propagates downstream, not automatically upstream.

This page lists public-facing load-bearing claims only. The full DT/FDS claim-space is archived in the DT Archive and Physical Bridge Claim Registry.

A claim appearing here is not asserted as equally established. Each claim is assigned a layer, dependency, failure condition, and consequence.

Core Bridge Operational Domain Bridge High-Risk

ID	Claim	Layer	Dependency	Failure
FDS-0	Active finite systems maintain boundaries under finite capacity.	Core	Formal definitions	Mathematical counterexample under stated hypotheses.
FDS-B	Active boundary maintenance distinguishes active finite systems from passive mappings.	Core	Boundary variable + update participation	Boundary update ablation has no effect on future maintenance loss.
CC-1	Capacity deficit arises under finite representation and incompressible task demand.	Core	Finite capacity + task demand	Finite system maintains lossless model of incompressible environment under bounded capacity.
CC-2	Capacity deficit forces approximation under bounded representation.	Core	Finite capacity + nontrivial task demand	Bounded systems maintain exact task-relevant representation without compression, omission, or distortion.
CC-3	Approximation generates residual error requiring correction or tolerance.	Core	Approximation + task loss	Approximation produces no residual burden under nontrivial task constraints.
CC-5	Persistent capacity deficit drives pruning, externalization, task relaxation, or collapse.	Core	Capacity deficit + finite resources	Persistent deficit produces none of the predicted response modes.
CC-6	Long-term persistence is favored by invariant-supported structure.	Core	Perturbation family + identity predicate	Structures persist without invariant support under sustained perturbation.
PB-FD	Physically instantiated identity maintenance requires finite distinguishability budgets.	Bridge	Finite physical resources / bounded records	A physical system maintains unlimited usable distinguishability within finite resources.
PB-L	Logically irreversible updates incur a thermodynamic cost under Landauer bridge assumptions.	Bridge	Standard Landauer conditions	Reliable irreversible erasure below the thermodynamic floor under stated conditions.
O1	An observer can be characterized as a finite distinction register.	Bridge	Finite record capacity	Measurement records require no finite registration or boundary-stabilized state.
O2	Time can be characterized as irreversible distinction update.	Bridge	Truncation + irreversible update	Finite record-updates are fully invertible under bounded memory in physical implementation.
O3	Finite-memory operational Second-Law channel for boundary-maintaining active finite systems.	Bridge	Finite memory + irreversible record reuse + accounting boundary	Sustained residual record turnover at fixed tolerance with no ledger cost and no exit channel under physical bridge assumptions.
O3-001	Finite memory creates record-reuse pressure under sustained update unless history is externalized, compressed, uncomputed, abandoned, or resources expand.	Bridge	Finite memory capacity; O2 register time	Bounded-memory system maintains unbounded usable history internally without reuse, external memory, compression, or failure.
O3-002	Non-injective record reuse creates residual irreversibility relative to an accounting boundary.	Bridge	O3-001; O1 finite record formation	Many-to-one update preserves full preimage information without side records or enlarged boundary.
O3-003	Physical irreversible record reuse enters an entropy/resource ledger under bridge assumptions.	Bridge	O3-002; P1 Landauer bridge	Reliable physical erasure or overwrite violates Landauer-style accounting under stated assumptions.
O3-004	Stable finite records require housekeeping beyond logical erasure.	Bridge	O3-003; P2 garbage entropy rate	Refresh, retention, clocking, synchronization, carrier repair, and verification cost-free in every implementation.
O3-005	Externalization shifts the operational Second-Law channel across accounting boundaries.	Bridge	O3-003; P1 accounting boundary	External records impose no write, verification, retrieval, latency, maintenance, or environmental cost.
O3-006	Pruning and invariant compression can reduce future entropy pressure when task identity is preserved.	Bridge	O3-004; T3 Phase-B invariants	No task-preserving quotient, pruning, or compression ever reduces future record-maintenance cost.
O3-007	Sustained residual record turnover, fixed boundary tolerance, and zero coupled entropy/resource cost cannot persist indefinitely.	Bridge	O3-001--006	Finite active-boundary system maintains sustained residual turnover at fixed tolerance with no ledger cost and no exit channel.
O3-008	Topological or invariant persistence redirects entropy accounting rather than violating the Second Law.	Bridge	O3-003; Core invariant-supported persistence	Protected invariant supplies perpetual work or global entropy-law violation rather than bounded persistence or entropy relocation.
A1	Passive mappers do not qualify as strong FDS-agents.	Operational	Boundary, update, resource, and persistence criteria	Update ablation does not affect future boundary-maintenance loss.
A1-D	Strong FDS-agency requires resource-governed persistence.	Operational	FDS tuple + persistence test	System satisfies task output competence without durable update or boundary maintenance.
A1-C	FDS-agency requires action-to-future-state causal influence.	Operational	Intervention / transfer influence test	Actions have no measurable influence on future boundary-relevant states.
A1-E	Capacity-deficit estimation is required to distinguish scaling from agency.	Operational	Task demand + system capacity estimate	Systems qualify as agents without measurable boundary-relevant capacity pressure.
B1-1	Immune systems can be modeled as finite-capacity boundary-verification architectures.	Domain Bridge	B0 biomedical bridge governance; FDS core capacity definitions	Immune response can be fully organized without finite classification, memory, resource, boundary, or verification roles.
B1-2	Immune action requires admission and classification of candidate distinctions before downstream response.	Domain Bridge	B1-1; recognition-admission-verification-action pipeline	Action is empirically independent of admission, classification, memory, or context in the specified model.
B1-3	Immune classification is better modeled as a boundary-state vector than as a single self/non-self label.	Domain Bridge	B1-1; multiaxis classification	A one-dimensional label captures all relevant verification behavior in the declared system.
B1-4	High candidate-distinction load should produce delay, broad default action, reduced specificity, false positives/negatives, or FDS-resolution failure.	Domain Bridge	B1-1; verification saturation; VLR control number	Increasing verification burden produces no change in accuracy, delay, alarm load, resource use, or resolution.
B1-5	Immune memory reduces future verification cost but can produce drift, overgeneralization, or tolerance risk.	Domain Bridge	B1-1; memory-tolerance tradeoff	Memory has no measurable cost, drift, or threshold effect in the declared system.
B1-6	Some perturbations actively consume verification capacity or modify classification (adversarial sabotage).	Domain Bridge	B1-1; adversarial distinction injection model	Evasion-like processes never alter Y, pi, M, Phi, or C_verify in declared models.
B1-7	Immune verification is constrained by routing, migration, amplification, and return times (distributed spatial latency).	Domain Bridge	B1-1; spatial latency graph model; SLR control number	Spatial latency has no measurable effect in systems where local damage timescale is shorter than verification time.
N1	Self-organization as boundary maintenance under finite capacity.	Domain Bridge	FDS core definitions; finite capacity; budget exits	Freezing internal update has no effect on future boundary loss.
N1-001	Active self-organization requires boundary-maintenance-relevant internal update.	Domain Bridge	Active boundary criterion; finite capacity	System classified active even when update ablation has no effect on future boundary loss.
N1-002	Effective organizational capacity is task-relative and reduced by coordination, verification, latency, resource, and externalization costs.	Domain Bridge	Finite capacity; bottleneck logic	Boundary tasks maintained at full fidelity when all capacity factors fall below demand.
N1-003	Capacity deficit creates maintenance-load pressure, not necessarily raw complexity growth alone.	Domain Bridge	Capacity deficit; maintenance load equation	Increasing task demand never increases maintained load in any implementation.
N1-004	Unbounded Phase-A growth is impossible under finite resource input without exit channels.	Domain Bridge	Finite resource envelope; exit channel taxonomy	Active finite systems grow maintained load forever under finite resources with no exit.
N1-005	Pruning has a viability window and is resource-gated.	Domain Bridge	Resource-gated pruning equation	Pruning strength has no systematic effect on overload or persistence across controlled cases.
N1-006	Externalization shifts rather than removes boundary-maintenance burden, and can clog the environment.	Domain Bridge	Accounting boundary; externalization ROI equation	External records impose no storage, verification, retrieval, or repair burden in any implementation.
N1-007	Phase-C catastrophic feedback couples boundary loss with resource depletion.	Domain Bridge	Resource and loss dynamics; positive loop gain	Resource depletion and boundary loss never couple positively in collapse-prone systems.
N1-008	Phase-B residues are biased toward low-maintenance, task-relevant invariants.	Domain Bridge	T3 Phase-B invariants; survival score function	Residues after overload show no bias toward reduced maintenance cost or task relevance.
S1	Organizations and civilizations can be modeled as active finite distinction systems.	Domain Bridge	Institutional boundary + memory + resource budget	Persistent institutions avoid collapse under unlimited complexity growth without pruning, externalization, or reform.
P3	Environmental forgetting: finite baths have limited accessible recovery capacity.	Physical bridge	FDS core finite capacity; P4 preimage loss	Finite accessible environment preserves unbounded side records indefinitely with no cost or degradation.
P3-001	Environmental side records have finite accessible recovery capacity.	Physical bridge	FDS-CORE-003; FDS-CORE-005	Finite system recovers unbounded inverse information from environment through a finite observation channel with no latency or cost.
P3-002	Markovianization is an effective forgetting condition.	Physical bridge	P3-001; lumpability condition	Projected process treated as Markovian while accessible history measurably improves prediction or boundary maintenance.
P3-003	Memory kernels measure unresolved environmental memory.	Physical bridge	P3-001; projection operator methods	Eliminated variables never reappear as memory, noise, or closure error despite coupling and non-lumpable projection.
P3-004	Finite baths can remember, forget operationally, and recur.	Physical bridge	P3-001; finite bath capacity	A finite bath is always exactly Markovian and never returns correlations under any admissible model.
P3-005	Environmental forgetting complements P4 internal truncation.	Physical bridge	P3-001; P4-001	Internal preimages lost yet environmental side records remain fully accessible indefinitely with bounded cost.
P3-006	Bath saturation forces collisions, compression, or loss of recoverability.	Physical bridge	P3-001; bath record capacity	Finite accessible bath stores more records than its capacity without collision, compression, or erasure.
X1	High-risk bridge hypothesis: horizon-maintenance dark energy under finite distinguishability budgets.	High-Risk	Cosmological bridge assumptions	Observations force exact Lambda behavior beyond stated tolerance.
P5	Deficit-driven entropy-production ledger for active finite systems.	Bridge	FDS core definitions; Landauer bridge; accounting boundary	Sustained positive deficit shows zero measurable physical cost under controlled conditions.
P5-001	Capacity deficit is task-relative information shortfall, not thermodynamic entropy.	Bridge	Rate-distortion demand; effective capacity	Not empirical (boundary statement separating formal from physical).
P5-002	Sustained deficit plus boundary maintenance requires correction, externalization, or failure.	Bridge	Budget exits; deficit definition	Finite system maintains task at fixed tolerance despite deficit and no correction or exit.
P5-003	Physical correction cycles induce audit channels through update, refresh, repair, synchronization, externalization, and transport.	Bridge	Carrier criterion; accounting boundary	Sustained correction, refresh, repair, and sync at zero entropy or resource cost.
P5-004	Logical erasure contributes a Landauer-style entropy-production floor under bridge assumptions.	Bridge	Landauer bridge; correction channels	Logically irreversible erature violates Landauer lower bound under stated assumptions.
P5-005	Housekeeping entropy persists even when logical erasure is zero.	Bridge	Reversible embedding; carrier maintenance	Boundary maintenance, refresh, clocking, sensing, and repair cost-free when erasure is zero.
P5-006	Externalization shifts rather than removes the entropy ledger.	Bridge	Accounting boundary; externalization audit	External records impose no write, verification, retrieval, sync, or maintenance cost.
P5-007	Pruning and invariant compression can reduce future entropy-production pressure.	Bridge	T3 Phase-B invariants; pruning ROI model	No task-preserving simplification ever reduces refresh, repair, or verification cost.
P5-008	Deficit crossing predicts measurable signatures in heat, resource use, latency, resets, or error floor.	Bridge	Deficit-crossing protocol; ledger decomposition	Positive deficit sustained with no measurable change in any physical or task channel.
P4	Coarse-grained anti-recurrence: capacity recovery is not distinction recovery.	Physical bridge	FDS core finite capacity; FDS finite projection	Exact preimage recovery from truncated record alone without side records or hidden inverse information.
P4-001	Non-injective truncation creates preimage uncertainty relative to the effective record.	Physical bridge	FDS finite projection	A many-to-one map contains enough information without side records to distinguish all of its preimages.
P4-002	Bayes-optimal guaranteed exact preimage recovery is bounded by the largest conditional preimage mass.	Physical bridge	P4-001; Bayes decision theory	A decoder using only Z exceeds the Bayes-optimal classifier bound for X\|Z.
P4-003	Capacity recovery does not recover distinctions erased during a bottleneck.	Physical bridge	P4-001; side-record criterion	Finite system recovers exact task-relevant preimage distinctions after capacity restoration with no side record.
P4-004	Non-lumpable coarse-graining creates hidden-state memory and effective stochasticity.	Physical bridge	P4-001; lumpability condition	A non-lumpable projection closes exactly on Z_t alone without hidden state or extra variables.
P4-005	Projection-induced memory burden has a Mori-Zwanzig analogue.	Physical bridge	P4-004; Mori-Zwanzig formalism	Eliminated variables never reappear as memory, noise, or closure error when lumpability fails.
P4-006	Externalization restores inverse information only by moving it to a side ledger.	Physical bridge	P4-001; external cost model	External logs restore exact recovery at no writing, retention, or boundary-expansion cost.
P4-007	Sustained truncation requires residual irrecoverability, side records, externalization, task relaxation, or failure.	Physical bridge	P4-001; P4-003	Finite system repeatedly applies non-injective truncation while preserving exact recovery with no residual uncertainty.
P7	Topological obstruction: some task distinctions are protected against local forgetting by invariant structure.	Physical bridge	P4-001; invariant quotient map; NHSE model class	Invariant fails to suppress residual uncertainty, or local perturbation erases protected sector without protection-breaking event.
P7-001	Invariant side-ledgers can suppress P4 residual inverse uncertainty.	Physical bridge	P4-001; invariant quotient map	Task variable factors through accessible invariant but H(V\|Z,Q_inv) remains high.
P7-002	Noisy invariant readout gives a bounded recovery penalty via Fano bound.	Physical bridge	P7-001; Fano bound	Noisy readout exceeds Fano bound without hidden information or changed task labels.
P7-003	Local perturbations cannot change a protected invariant without a protection-breaking event.	Physical bridge	P7-001; local perturbation family; protection margin	Local perturbation changes invariant while protection gap and accounting boundary remain intact.
P7-004	NHSE supplies a model class for invariant-supported persistence.	Physical bridge	P7-003; point-gap winding; GBZ structure	NHSE present but carries no stable recoverable distinction or boundary-sensitive protection.
P7-005	Protection relocates entropy/resource accounting rather than deleting it.	Physical bridge	P7-001; O3 ledger principle	Protected invariant supplies indefinite maintenance with no drive or external ledger.
P7-006	Protected phases can generate a dual forgetting/ledger signature.	Physical bridge	P7-004; P7-005; operational forgetting rate	Protection-breaking transition with no feature in operational forgetting and no ledger signature.
P8	Residue spectral dynamics: hidden unresolved modes couple to observable dynamics via memory kernels in finite systems.	Physical bridge	P3 finite-bath memory; P4 anti-recurrence; P5 entropy ledger; P6 throughput bounds; spectral decomposition	Residue channels have no measurable effect on observable dynamics under valid finite-system mapping; memory-kernel closure fails at declared tolerance.
P8-001	Hidden unresolved modes form residue channels (excitation, evolution, return) in finite distinction systems.	Physical bridge	P8; Mori-Zwanzig projection; spectral decomposition	No systematic triple (excitation, evolution, return) identifiable under controlled finite-system conditions.
P8-002	Residue qualification hierarchy separates active, dormant, and inactive unresolved modes.	Physical bridge	P8-001; spectral gap analysis	Qualification hierarchy does not predict dynamical recovery or closure behavior.
P8-003	Exponential-stability closure bounds exist for finite-window residue dynamics.	Physical bridge	P8-001; balanced truncation; Hankel operators	Declared stability bounds violated in controlled finite-sample tests.
P8-004	Marginal-mode obstruction prevents exact Markov closure for generic finite systems.	Physical bridge	P8-001; spectral-edge asymptotics	Generic finite systems admit exact Markovian closure without residue error.
P8-005	Finite-window Hankel significance detects residue mode contribution operationally.	Physical bridge	P8-001; P8-003; Hankel singular values	Hankel significance does not correlate with residue recovery error in controlled tests.
P8-006	P8 completes the P3-P4-P5-P6-P7-P8 residue bridge sequence for finite distinction systems.	Physical bridge	P3 environmental forgetting; P4 anti-recurrence; P5 entropy ledger; P6 throughput; P7 topological protection; P8 spectral dynamics	Sequence has systematic gaps or redundant components under unified finite-system accounting.
P8-007	Coupled residue channels: excitation, evolution, and return define Markov closure regimes via spectral dynamics.	Physical bridge	P3-P4-P5-P6-P7; controllability, observability, transfer functions, semigroup decay estimates	Residue channels have no measurable effect on observable dynamics; qualification hierarchy does not predict dynamical recovery; marginal-mode obstruction is absent in generic finite systems.
P8-008	Operational recoverability and memory-burden bounds depend on transfer significance, Hankel singular values, and observation channels, not on residue lifetime alone.	Physical bridge	P4 pre-image observability; P8 channel registration; decoder specification; strictly proper rational kernels	Recovery is obtained only by changing the accounting boundary, decoder resources, or observation channel; non-rational kernel asserted to have finite exact realization.
P6	Speed-precision-dissipation bounds: boundary maintenance requires finite update throughput.	Physical bridge	FDS core finite capacity; P4 anti-recurrence; P7 invariant quotient	Finite system maintains arbitrarily fast and precise boundary tasks at fixed capacity and fixed resource with no extra cost.
P6-001	Boundary maintenance requires finite update throughput.	Physical bridge	FDS finite capacity; finite projection	A time-varying boundary is maintained without updating or acting on any task-relevant distinction.
P6-002	Speed and precision jointly increase maintenance burden.	Physical bridge	P6-001; rate-distortion demand	Faster and more precise maintenance sustained indefinitely at fixed representation and fixed resource.
P6-003	The sustainable internal rate is bottlenecked by sensing, updating, verification, correction, action, and resources.	Physical bridge	P6-001; P6-002	System exceeds slowest internal channel indefinitely without queueing, latency, or loss.
P6-004	Correction and verification belong in the resource ledger.	Physical bridge	P6-001; P6-003; O3 ledger principle	Physical correction, refresh, and verification are cost-free under stated implementation assumptions.
P6-005	Effective causal update bandwidth limits real-time maintenance.	Physical bridge	P6-001; finite causal reach	Finite observer integrates arbitrarily distant information within a finite update window with no latency.
P6-006	Externalization and invariant compression are relief channels, not free exits.	Physical bridge	P6-001; P4 side-record criterion; P7 invariant quotient	External ledgers or invariant quotients reduce internal demand with no coupled cost.
P6-007	If rate-distortion demand exceeds sustainable internal throughput, the system must enter an exit channel or fail.	Physical bridge	P6-001–006	Demand exceeds throughput with no exit channel and no boundary failure under a valid mapping.
FDS-A1-001	An artificial agent is an active finite distinction system maintaining boundary through durable updates.	Conceptual criterion	FDS-CORE-002; FDS-CORE-003; FDS-CORE-004; FDS-CORE-005
FDS-A1-002	Public programme retains FDS-A1 as conceptual timestamp; no proprietary AI development in repo.	Governance	FDS core
FDS-CORE-001	A distinction is an operation or relation that separates at least two alternatives within a possibility space.	Formal definition	FDS core	Not falsified in usual sense; usefulness can fail.
FDS-CORE-002	Once a system distinguishes itself from what it is not, it inherits a boundary.	Formal definition	FDS-CORE-001	Bounded system with zero maintenance cost under sustained load.
FDS-CORE-003	A finite system with a boundary has finite representational and operational capacity.	Formal/operational claim	FDS-CORE-002	Physically instantiated bounded system with infinite operational capacity.
FDS-CORE-004	When task-relevant distinction demand exceeds accessible capacity, the system operates under a capacity deficit.	Formal definition	FDS-CORE-003
FDS-CORE-005	A finite system under persistent positive capacity deficit must prune, externalize, relax the task, compress, or collapse.	Conditional theorem	FDS-CORE-004
FDS-CORE-006	Systems that persist under finite capacity do so by maintaining invariants that reduce effective distinction load.	Conditional theorem	FDS-CORE-005	Persistent system under sustained deficit with no invariant-supported load reduction.
FDS-LC0-001	FDS-LC0 registers life/cognitive bridge claims with dependencies, risks, and failure conditions.	Registry governance	FDS core
FDS-LC0-002	Failure of life/cognitive bridge does not propagate to upstream physical bridges or core.	Registry governance	FDS core
FDS-T1-001	A finite physical observer O can operationally use only a finite image Im(pi_O) of a physical possibility space.	Operational/physical bridge claim	FDS core	Observer with unbounded distinctions under finite resources.
FDS-T1-002	Operational distinguishability is bounded by minimum of internal record capacity and accessible boundary/channel capacity.	Conditional theorem	FDS-T1-001
FDS-T1-003	Accessible capacity separates into stock capacity and update throughput; effective task capacity is their minimum.	Formal definition/Conditional theorem	FDS-T1-002
FDS-T1-004	Delta_FDS = R_min - C_acc where R_min is task demand and C_acc is accessible capacity.	Definition	FDS-T1-003
FDS-T1-005	If Delta_FDS > 0 persists, observer must enter at least one exit class.	Conditional theorem	FDS-T1-004; FDS-CORE-005
FDS-T1-006	Positive deficit implies Landauer-style lower bound on thermodynamic maintenance cost for irreversible erasure.	Conditional physical bridge	FDS-T1-005
FDS-T1-007	As chi = R_min - C_acc crosses zero, observers should show measurable transitions.	Testable prediction	FDS-T1-005
FDS-T1-008	Rate-distortion error floor shows slope discontinuities at bottleneck switches.	Conditional theorem	FDS-T1-003
FDS-X1-001	Cosmological horizons act as finite distinguishability boundaries for observers.	Frontier Physical Consequences	FDS-T1-001; FDS-T1-002
FDS-X1-002	Horizon-maintenance cost has scale rho ~ H^2 M_Pl^2, consistent with dark energy.	Frontier Physical Consequences	FDS-X1-001
FDS-X1-003	Equation of state tends toward w=-1 from above (non-phantom) with possible mild evolution.	Frontier Physical Consequences	FDS-X1-002
FDS-X1-004	X1 claims have explicit falsification conditions stated in advance.	Governance	FDS-X1-001; FDS-X1-002; FDS-X1-003
X2	CKM-type CP violation requires NCKM >= 3; weak identity transformation needs CP/T orientation.	Frontier Physical Consequences	FDS core finite capacity; Kobayashi-Maskawa CKM phase counting	CKM-like two-generation weak sector shown to possess a physical irreducible CP phase; weak-sector identity-changing channel realized without CP/T orientation.
X2-001	For a CKM-type N×N unitary charged-current mixing matrix, an irreducible physical complex phase exists iff N>=3.	High-risk	KM 1973; unitary matrix algebra	CKM-like two-generation weak sector shown to possess a physical irreducible CP phase.
X2-002	Weak-sector identity transformation requires a rephasing-invariant CP/T orientation.	High-risk	FDS-X2-001; CPT theorem	Complete physical account of weak identity-changing channel with no CP/T orientation and no compensating asymmetry.
X2-003	The weak charged current is the Standard Model identity-transformation carrier.	High-risk	FDS-X2-002; Standard Model flavor physics	Identity-changing weak-sector operations realized by a different physical carrier outside the CKM charged current.
X2-004	NCKM>=3 follows from the X2 chain: weak identity update → T/CP orientation → irreducible CKM phase.	High-risk	FDS-X2-001; FDS-X2-002; FDS-X2-003	Failure of any premise: CP/T-orientation bridge, CPT assumptions, weak-carrier mapping, or CKM phase counting.
X2-005	Exactly three sequential chiral generations follow from minimality.	High-risk	FDS-X2-004; flavor-cost functional	Discovery of a fourth sequential chiral generation with SM gauge charges and weak charged-current participation.
X2-006	X2 motivates a nonzero leptonic Dirac CP phase under stated assumptions.	High-risk	FDS-X2-002; PMNS phenomenology	High-precision data establish delta_CP=0 or pi under assumptions requiring leptonic CP/T-oriented identity transformation.
X3	Four known interactions form a minimal distinction-operation closure for finite physical systems.	Frontier Physical Consequences	FDS core; QCD; QED; electroweak; GR	Stable tokens exist without encapsulation; complex structure exists without connection/detectability; identity-sector transitions exist without transformation/update; new fundamental interaction adds irreducible operation class.
X3-001	Finite distinction systems require token stabilization.	High-risk	FDS core; distinction persistence requirement	Stable material tokens exist with no encapsulation or stabilization mechanism.
X3-002	The strong interaction realizes hadronic/baryonic encapsulation.	High-risk	X3-001; QCD	Hadronic stability explained while confinement plays no token-stabilizing role.
X3-003	Finite distinction systems require remote detectability and compositional connection.	High-risk	FDS core; X3-001	Complex persistent structures form without any mediating interaction enabling detectable coupling.
X3-004	Electromagnetism realizes connection and communication among charged sectors.	High-risk	X3-003; QED	EM shown not to underwrite chemistry, radiation, or long-range communication.
X3-005	Finite distinction systems require identity transformation and selective update.	High-risk	FDS core; X3-001; X3-003	Physical identity sectors never require conversion, decay, or irreversible update.
X3-006	The weak interaction realizes identity transformation, flavor change, and unstable-state pruning.	High-risk	X3-005; electroweak theory; X2	Flavor change and weak identity transformation realized by another carrier.
X3-007	Gravity realizes global boundary / causal geometry / stress-energy accounting.	High-risk	X3-001; GR	Gravity shown unrelated to geometry, causal structure, or stress-energy accounting.
X3-008	The four interactions form a minimal distinction-operation closure.	High-risk	X3-001–007	A fundamental interaction implements a genuinely independent operation class not reducible to the four.
X4	Pauli exclusion is a collision-free fermionic mode-address occupancy rule that protects finite fermionic addresses and forces structural diversity.	Physical bridge	FDS core; nilpotent fermionic algebra; P6 causal reachability	Identical SM fermions occupy same complete quantum state; stable matter exists without exclusion; SM fermions exhibit generalized p>1 occupancy.
X4-001	Fermionic creation operators obey nilpotency (a_i^dag)^2 = 0, enforcing single-occupancy fermionic mode addresses.	Standard quantum algebra	Canonical anticommutation relations	Identical SM fermions observed occupying same complete quantum state.
X4-002	Pauli exclusion protects single-fermion mode-address occupancy.	FDS interpretation	X4-001	Fermionic matter remains address-stable without single-address occupancy protection.
X4-003	Exclusion forces structural diversity in fermionic matter.	Physical / operational	X4-002	Electrons occupy same atomic state while shell structure unchanged.
X4-004	Matter stability depends on fermionic antisymmetry.	Standard mathematical physics	X4-003; Dyson-Lenard; Lieb-Thirring	Stability proven without exclusion-like antisymmetry.
X4-005	Bosonic multiple occupation is not an X4 violation.	Conceptual caveat	X4-001; BEC	Bosonic occupation creates multiple independently address-protected fermionic events at same address.
X4-006	The Pauli rule n_i ∈ {0,1} is the minimal address-protection rule for ordinary 3+1D SM fermions.	Minimality bridge	X4-002; generalized statistics	SM fermions obey generalized p>1 occupancy, or lower-overhead alternative realized.
X4-007	Degeneracy pressure is macroscopic address protection.	Physical bridge	X4-002; Chandrasekhar; TOV	White-dwarf support occurs without degeneracy pressure.
X4-008	Address scarcity follows from the finite causal reachability boundary.	Physical bridge (P6 connection)	X4-002; FDS-P6	Address scarcity and structural diversity exist without causal horizon bound.
X5	Mathematical form of physical law is invariant-form compression: portable law-like regularities factor through invariant, equivariant, or covariant sectors.	Invariant-form compression bridge	FDS core; invariant quotients; symmetry/group theory	Stable physical laws exist that cannot be represented by any invariant/equivariant/covariant compressed relation; finite systems maintain law-like prediction without reducing raw complexity.
X5-001	Finite systems cannot internally represent all microstate detail.	Formal FDS core	FDS core; finite capacity theorem	Finite system internally represents unbounded environmental distinctions with no compression.
X5-002	Stable law-like regularities require invariant-form compression.	FDS structural claim	X5-001	Portable regularities persist with no invariant/equivariant/covariant form or compressed relation.
X5-003	Mathematical equations are compressed invariant-form relations.	Interpretive bridge	X5-002	Exact physical laws require no compression or form stability.
X5-004	Symmetries reduce rule-maintenance cost.	Physical / information bridge	X5-002	Asymmetric rules are cheaper and more stable than invariant/equivariant compressed rules.
X5-005	Wigner's puzzle is reframed by invariant-form compression.	Philosophical bridge	X5-002; X5-003	Mathematics remains effective for law-like physics where no invariant/equivariant/covariant compression exists.
X5-006	Constants such as e, i are model-class signatures.	Optional bridge	X5-002	Their appearance is asserted as universal without model-class assumptions.
X5-007	Open math problems may have physical analogues.	Speculative appendix	X5-002	Analogues are mistaken for derivations or proofs.
X5-008	RG fixed points are invariant-form compression under coarse-graining.	Physical bridge	X5-002; Wilson RG	All physical law reduces strictly to RG fixed points; or no law-like relation survives coarse-graining.
T2-001	Finite observers have bounded distinguishability budgets.	Bridge	FDS-T1	A finite physical observer reliably registers, preserves, and updates unlimited distinctions with finite resources.
T2-002	Horizons act as causal-access boundaries.	Bridge	General relativity	Local causal horizons are irrelevant to observable access, entropy, or thermodynamic accounting.
T2-003	Horizon entropy gives boundary area accounting.	Physical bridge	Bekenstein-Hawking	Horizon entropy is shown not to scale with boundary area in the stated horizon class.
T2-004	Clausius-type local horizon closure links heat flow and entropy variation.	Model-class bridge	Jacobson 1995	Local horizon thermodynamics fails as an effective equation-of-state model.
T2-005	Effective geometry can be read as boundary thermodynamic accounting.	Main T2 thesis	T2-001–004	Geometry is shown to have no relation to causal access, horizon entropy, stress-energy flow, or boundary constraints.
T2-006	Non-equilibrium horizon accounting may require residual terms.	Optional extension	T2-005	All non-equilibrium horizon settings obey pure equilibrium closure with no entropy production, memory, noise, or correction terms.
Q1-001	Observers are finite distinction-registers.	O1 operational bridge	FDS-O1	Registered observations require no finite carrier, boundary, readout, record stability, or update capacity.
Q1-002	Operationally assertable quantum facts are indexed by accessible record boundaries.	Q1 bridge	Q1-001	Operational facts can be asserted by a finite observer without any stable accessible record or reproducible trace.
Q1-003	Wigner-friend tension is a boundary-promotion problem.	Main Q1 thesis	Q1-001; Q1-002	Contradictions persist after all accessible record boundaries, channels, and state-assignment domains are separated.
Q1-004	Friend-relative records require mutual information before promotion into Wigner's algebra.	Information-theoretic bridge	Q1-003	A Wigner-accessible fact is obtained with vanishing cross-boundary mutual information and no physical record channel.
Q1-005	Wigner's ignorance is not physical coherence.	Scope firewall	Q1-001	The paper is interpreted as inferring coherent lab states from missing classical information alone.
Q1-006	Objective availability requires redundancy, access, and record stability.	Testable bridge hypothesis	Q1-003; quantum Darwinism	Observers converge on macroscopic records without redundancy, access, or stable records.
Q1-007	Q1 does not derive Born probabilities.	Scope firewall	Q1-001	The paper is interpreted as a probability or Born-rule derivation rather than a conditional record-availability theory.
Q2-001	Logical qubits are protected quantum distinctions.	FDS/QI bridge	FDS core; QEC theory	Logical information cannot be represented as a protected code quotient or logical algebra.
Q2-002	QEC is active finite-distinction maintenance.	Main Q2 interpretation	Q2-001	Logical distinctions are preserved under noise with no redundancy, syndrome information, feedback, passive protection, or maintenance channel.
Q2-003	Threshold theorem is accepted as conditional baseline.	Scope firewall	Threshold theorem	The paper is read as refuting the threshold theorem rather than auditing its physical assumptions.
Q2-004	Correction demand is a vector ledger.	Engineering bridge	Q2-002	Syndrome, decoding, reset, latency, cooling, and control demands can be collapsed into one scalar without losing bottleneck information.
Q2-005	Irreversible reset has a Landauer lower bound.	Physical bridge	Landauer 1961	Reliable logically irreversible reset below kT ln2 per erased bit under standard Landauer conditions.
Q2-006	Cryogenic solid-state systems face cold-stage ledger constraints.	Architecture-specific claim	Q2-004; Q2-005	Large-scale cryogenic processors maintain falling logical error while all cold-stage power, routing, latency, and reset ledgers remain within budget.
Q2-007	Topological/passive protection can reduce but not eliminate active load.	Escape-channel bridge	Q2-002	Passive protection removes preparation, finite-temperature, readout, braiding, leakage, and residual correction costs entirely.
Q2-008	Q2 failure does not falsify FDS Core or Q1.	Failure propagation rule	Q2-001; Q2-002	Architecture-specific failure is treated as failure of the formal finite-system core or quantum mechanics.
B0-001	Finite observer bound applies to biomedical knowledge.	Formal bridge	FDS Core	Biomedical knowledge is acquired and maintained without any finite carrier, memory, or update constraint.
B0-002	Biomedical FDS mapping is modeling, not diagnosis.	Governance firewall	B0-001	The mapping is interpreted as clinical diagnosis without independent validation.
B0-003	B-series claims are domain bridges.	Governance firewall	B0-002	B-series claim is treated as proven clinical fact without biomedical validation.
B0-004	Claim-level hierarchy (B-L0 to B-L5) governs interpretation.	Registry governance	B0-003	A lower-level claim is cited as if it were clinically actionable.
B0-005	Translation barrier prevents clinical overreach.	Safety firewall	B0-004	FDS biomedical language is used in clinical decision-making without independent validation.
B0-006	Mechanism non-replacement rule.	Governance rule	B0-001	FDS classification is used to replace validated biomedical mechanisms.
B0-007	Maintenance debt as accumulated repair-verification mismatch.	Non-clinical concept	B0-001	Maintenance debt is treated as a clinical biomarker before validation.
B0-008	B0 failure does not falsify FDS Core.	Propagation rule	B0-001	B-series failure is interpreted as failure of the formal FDS core.
H1-001	Holography is finite boundary distinction recovery under screen-capacity constraints.	Physics — H-series	Standard AdS/CFT, RT/FLM, holographic QEC, Bousso covariant entropy bound	Finite boundary recovery cannot be captured by screen capacity, recovery nets, or gluing obstruction diagnostics.
H1-002	On each connected component of the nerve graph of a finite cover, path-independent recovery holds iff all cycle holonomies vanish.	Physics — H-series	H1-001	Recovery consistency cannot be captured by loop holonomy or gluing obstruction in finite models.
H1-003	Under Lipschitz transition maps, recovery error accumulates as product-weighted sum; 1-Lipschitz corollary gives simple triangular error bound.	Physics — H-series	H1-002	Finite recovery error bounds cannot be established under Lipschitz or non-expansive transition maps.
H1-004	There exist finite boundary ledgers with identical local marginal entropy H(B_i) but different recovery errors for the same bulk distinction.	Physics — H-series	H1-001	Recovery error is entirely determined by local marginal boundary entropy in all controlled finite models.
Q0-001	Physical distinguishability is first directed boundary access.	Physics — Quantum upstream	FDS core	All operational record production, erasure, and recovery are symmetric without boundary cost or accessibility structure.
Q0-002	Zero record holonomy makes the reversible quotient well-defined; in the restricted quantum-access category the induced kernel is symmetric.	Physics — Quantum upstream	Q0-001	A closed, record-neutral, zero-holonomy sector fails to admit any well-defined symmetric quotient kernel.
Q0-003	Hilbert quantum mechanics is the finite-capacity zero-holonomy sector.	Physics — Quantum upstream	Q0-002	A non-Hilbert reciprocal finite-capacity quotient satisfies reversible dynamics, composition stability, and no hidden record asymmetry.
Q0-004	Born weights are the no-record-capacity-arbitrage rule.	Physics — Quantum upstream	Q0-003	A non-Born rule satisfies basis neutrality, coarse-graining, composition, and finite record-capacity no-arbitrage.
Q0-005	Decoherence irreversibility tracks stable records, not mere entanglement alone.	Physics — Quantum upstream	Q0-001	Stable record accessibility has no independent predictive role for recovery once ordinary overlap and noise metrics are controlled.
Q0-006	QEC overhead tracks directed leakage holonomy.	Physics — Quantum upstream	Q0-001	Directed leakage has no independent predictive value for logical failure after matched-fidelity and matched-syndrome controls.
H2-001	Raw exact descent, quotient descent, and strict liftability are distinct.	Physics — H-series	FDS-H1	A G0-valued defect does not guarantee quotient descent; a strict lift requires triviality of the associated twisted lifting obstruction.
H2-002	A connection must be generated by a pre-registered gauge-covariant rule.	Physics — H-series	H2-001	If curvature changes under equivalent presentations or response-dependent ambient geometry, it is not an identifiable support invariant.
H2-003	Kato transport is a recoverable-support geometry, not a full-channel geometry.	Physics — H-series	H2-002	Equal support projectors imply equal Kato connections and curvatures even when channel spectra, weights, fidelity, or action differ.
H2-004	The physical recovery quotient is a regular principal-bundle quotient.	Physics — H-series	H2-002	Outside the closed-normal, regular branch the quotient must be treated as stratified, orbifold, groupoid, or stack-like.
H2-005	The operational-covector bridge is domega_th = ell(F_phys) for a pre-registered parallel flat-coefficient readout.	Physics — H-series	H2-004	A global bridge requires [ell(F_phys)]_dR = 0; failure demotes the functional, scale calibration, or global covector realization.
H2-006	A parallel bundle bridge exists exactly when a base-point map intertwines all holonomies.	Physics — H-series	H2-004	Held-out loops support only the sampled subgroup unless generators are proved; does not apply to the direct covector branch.
H2-007	Parallel Branch-A readouts are holonomy-relative; character-based one-dimensional responses see only the full Lie-algebra Abelianization of the identity component.	Physics — H-series	H2-005	A general parallel readout annihilates [hol_X0, g_phys], not necessarily [g_phys, g_phys]; full Abelianization requires full-group invariance, a character differential, or equality of these commutator subspaces.
H2-008	H2 derives G1, GR, or M3/4.	Physics — H-series	H2-001	H2 ends at a support-level premetric response-obstruction criterion; full-channel geometry, Ward closure, optical selection, and cosmology remain downstream.
T3-001	Capacity overflow occurs when task-relevant distinction demand exceeds accessible capacity.	Physical Bridge	FDS-CORE-004 capacity deficit; task-relevant demand measure; accessible capacity measure	Full-fidelity tracking persists under bounded resources after independently estimated demand exceeds all accessible capacity.
T3-002	Non-injective projection induces effective stochasticity.	Physical Bridge	FDS-P4-001 non-injective truncation; deterministic or stochastic underlying dynamics; hidden successor variation within pre-image classes	A many-to-one accessible projection always induces deterministic accessible transitions despite hidden successors varying within the same visible record class.
T3-003	Overflow has a critical-deficit signature: predictive error and transition entropy show rapid increase near the capacity crossing.	Physical Bridge	FDS-T3-001 overflow definition; predictive error measure; transition entropy measure; controlled capacity crossing	Predictive error, transition entropy, and exit signatures vary smoothly through controlled capacity crossing with no susceptibility peak, kink, or rapid regime change.
T3-004	Phase-B variables are selected by low update cost, slow information decay, and approximate Markov closure.	Physical Bridge	FDS-T3-002 effective stochasticity; mutual information decay measure; Markov closure error measure; maintenance cost function	All coarse variables lose predictive information at the same rate under projection, regardless of update cost, closure error, or persistence utility.
T3-005	Capacity recovery need not reverse overflow: discarded distinctions are not automatically recovered.	Physical Bridge	FDS-P4-003 informational hysteresis; finite record capacity; no external recovery side-record	Discarded distinctions are perfectly reconstructed after capacity recovery without external logs, hidden reservoirs, or additional records.
T3-006	Stochastic descriptions are capacity-relative unless supported by capacity-independent noise sources.	Physical Bridge	FDS-T3-002 effective stochasticity; accounting boundary registration; capacity-independent noise source definition	The same process yields the same stochastic description independent of observer capacity, projection, measurement boundary, and retained memory.
T3-007	Long-context drift is a domain projection of wrong invariant completion under overflow.	Physical Bridge	FDS-T3-004 Phase-B invariants; context window capacity; false invariant completion mechanism	Context overflow in finite-window systems never increases false dependency, semantic drift, wrong task-state completion, or external-memory demand under matched tasks.
T4-001	Joint closure response includes both forced-history and preparation-coordinate input families.	Physical Bridge	FDS-P8 coupled residue channel; P3/P4 preparation/initial-data structure; registered preparation injection map	Preparation-forced residue has no measurable effect on closure quality or error budget.
T4-002	Active residue admits four admissible treatments: promote, localize, truncate, or reject.	Physical Bridge	FDS-P8 residue qualification hierarchy; finite task tolerance; closure error budget	Four-way taxonomy systematically misclassifies residue treatment decisions in controlled test cases.
T4-003	Closure operations do not commute: active quotient -> persistent isolation -> promotion -> stable reduction -> localization.	Physical Bridge	Ordered pipeline hypothesis; persistent-mode isolation before localization	Localization before persistent isolation yields identical or superior closure quality without divergence.
T4-004	Four-level state firewall distinguishes realization coordinates, physical closure states, macroscopic variables, and conserved quantities.	Physical Bridge	FDS-P7 side-ledger distinction; P3/P4 accessible/observer boundary; carrier registration	No measurable information-theoretic or physical difference between state categories under valid closure mapping.
T4-005	Persistent joint-response poles impose a minimum additional closure degree: additional closure degree >= McMillan degree of persistent block.	Physical Bridge	Minimal realization theory; rational transfer function McMillan degree; isolated persistent spectrum; joint forced-and-preparation response	An exact causal closure with fewer degrees than the persistent-block McMillan degree reproduces all registered joint responses.
T4-006	Additional closure degree is representation-invariant across internal state, higher-order derivatives, and registered side-ledgers.	Physical Bridge	FDS-T4-005 persistent-channel theorem; minimal linearization; full initial-data manifold	Equivalent joint responses with different representations have measurably different minimal linearized degrees.
T4-007	Operational promotion rank is monotonic in task window length, error tolerance strictness, and law-class restrictiveness.	Physical Bridge	Nested closure classes; contractive time-norm restriction; compatible input-window registration; finite-window Hankel operator	Promotion rank systematically decreases with longer task window, stricter tolerance, or smaller law class under valid registration.
T4-008	Fast-residue memory admits a startup-qualified Taylor expansion in derivatives of the retained state with controlled remainder.	Physical Bridge	Exponential semigroup bound; incomplete moment tail estimate; initial fast-residue forcing bound; retained-state regularity	Temporal localization with declared order violates error bound or diverges for valid stable memory kernels within stated assumptions.
T4-009	Local-truncation laws require separate stability audit: constitutive series convergence does not guarantee autonomous-law well-posedness.	Physical Bridge	Stable auxiliary-state reference; operator-pencil well-posedness criterion	All convergent Taylor expansions of stable memory kernels yield well-posed autonomous evolution laws.
T4-010	Phase-B closure frontier selects Pareto-minimal closures trading error, additional degree, law order, maintenance cost, and side-ledger access.	Physical Bridge	Multi-objective Pareto order; registered resource costs; certified error budgets	Pareto-optimal frontier does not correlate with actual closure quality or maintainability in controlled synthetic or experimental benchmarks.

Core Claims

FDS-0

Active finite systems maintain boundaries under finite capacity.

Dependency

Formal definitions

Failure

Mathematical counterexample under stated hypotheses.

Consequence

Revise formal core.

FDS-B

Active boundary maintenance distinguishes active finite systems from passive mappings.

Dependency

Boundary variable + update participation

Failure

Boundary update ablation has no effect on future maintenance loss.

Consequence

Revise active boundary criterion.

CC-1

Capacity deficit arises under finite representation and incompressible task demand.

Dependency

Finite capacity + task demand

Failure

Finite system maintains lossless model of incompressible environment under bounded capacity.

Consequence

Revise/demote capacity-deficit theorem.

CC-2

Capacity deficit forces approximation under bounded representation.

Dependency

Finite capacity + nontrivial task demand

Failure

Bounded systems maintain exact task-relevant representation without compression, omission, or distortion.

Consequence

Revise approximation theorem.

CC-3

Approximation generates residual error requiring correction or tolerance.

Dependency

Approximation + task loss

Failure

Approximation produces no residual burden under nontrivial task constraints.

Consequence

Revise error-correction claim.

CC-5

Persistent capacity deficit drives pruning, externalization, task relaxation, or collapse.

Dependency

Capacity deficit + finite resources

Failure

Persistent deficit produces none of the predicted response modes.

Consequence

Revise trichotomy.

CC-6

Long-term persistence is favored by invariant-supported structure.

Dependency

Perturbation family + identity predicate

Failure

Structures persist without invariant support under sustained perturbation.

Consequence

Revise invariant persistence claim.

Bridge Claims

PB-FD

Physically instantiated identity maintenance requires finite distinguishability budgets.

Dependency

Finite physical resources / bounded records

Failure

A physical system maintains unlimited usable distinguishability within finite resources.

Consequence

Demote physical bridge; formal core remains.

PB-L

Logically irreversible updates incur a thermodynamic cost under Landauer bridge assumptions.

Dependency

Standard Landauer conditions

Failure

Reliable irreversible erasure below the thermodynamic floor under stated conditions.

Consequence

Demote physical bridge; formal core remains.

An observer can be characterized as a finite distinction register.

Dependency

Finite record capacity

Failure

Measurement records require no finite registration or boundary-stabilized state.

Consequence

Demote observer bridge.

Time can be characterized as irreversible distinction update.

Dependency

Truncation + irreversible update

Failure

Finite record-updates are fully invertible under bounded memory in physical implementation.

Consequence

Revise time bridge.

Finite-memory operational Second-Law channel for boundary-maintaining active finite systems.

Dependency

Finite memory + irreversible record reuse + accounting boundary

Failure

Sustained residual record turnover at fixed tolerance with no ledger cost and no exit channel under physical bridge assumptions.

Consequence

Demote Second-Law bridge; O1/O2 record and register-time claims remain intact.

O3-001

Finite memory creates record-reuse pressure under sustained update unless history is externalized, compressed, uncomputed, abandoned, or resources expand.

Dependency

Finite memory capacity; O2 register time

Failure

Bounded-memory system maintains unbounded usable history internally without reuse, external memory, compression, or failure.

Consequence

Revise reuse-pressure claim.

O3-002

Non-injective record reuse creates residual irreversibility relative to an accounting boundary.

Dependency

O3-001; O1 finite record formation

Failure

Many-to-one update preserves full preimage information without side records or enlarged boundary.

Consequence

Revise residual irreversibility claim.

O3-003

Physical irreversible record reuse enters an entropy/resource ledger under bridge assumptions.

Dependency

O3-002; P1 Landauer bridge

Failure

Reliable physical erasure or overwrite violates Landauer-style accounting under stated assumptions.

Consequence

Demote ledger-entry claim.

O3-004

Stable finite records require housekeeping beyond logical erasure.

Dependency

O3-003; P2 garbage entropy rate

Failure

Refresh, retention, clocking, synchronization, carrier repair, and verification cost-free in every implementation.

Consequence

Demote housekeeping claim.

O3-005

Externalization shifts the operational Second-Law channel across accounting boundaries.

Dependency

O3-003; P1 accounting boundary

Failure

External records impose no write, verification, retrieval, latency, maintenance, or environmental cost.

Consequence

Revise externalization claim.

O3-006

Pruning and invariant compression can reduce future entropy pressure when task identity is preserved.

Dependency

O3-004; T3 Phase-B invariants

Failure

No task-preserving quotient, pruning, or compression ever reduces future record-maintenance cost.

Consequence

Demote pruning-relief claim.

O3-007

Sustained residual record turnover, fixed boundary tolerance, and zero coupled entropy/resource cost cannot persist indefinitely.

Dependency

O3-001--006

Failure

Finite active-boundary system maintains sustained residual turnover at fixed tolerance with no ledger cost and no exit channel.

Consequence

Revise impossibility triangle.

O3-008

Topological or invariant persistence redirects entropy accounting rather than violating the Second Law.

Dependency

O3-003; Core invariant-supported persistence

Failure

Protected invariant supplies perpetual work or global entropy-law violation rather than bounded persistence or entropy relocation.

Consequence

Demote topological projection; core remains intact.

Deficit-driven entropy-production ledger for active finite systems.

Dependency

FDS core definitions; Landauer bridge; accounting boundary

Failure

Sustained positive deficit shows zero measurable physical cost under controlled conditions.

Consequence

Demote entropy bridge.

P5-001

Capacity deficit is task-relative information shortfall, not thermodynamic entropy.

Dependency

Rate-distortion demand; effective capacity

Failure

Not empirical (boundary statement separating formal from physical).

Consequence

Revise deficit definition.

P5-002

Sustained deficit plus boundary maintenance requires correction, externalization, or failure.

Dependency

Budget exits; deficit definition

Failure

Finite system maintains task at fixed tolerance despite deficit and no correction or exit.

Consequence

Revise correction-pressure claim.

P5-003

Physical correction cycles induce audit channels through update, refresh, repair, synchronization, externalization, and transport.

Dependency

Carrier criterion; accounting boundary

Failure

Sustained correction, refresh, repair, and sync at zero entropy or resource cost.

Consequence

Demote audit-channel claim.

P5-004

Logical erasure contributes a Landauer-style entropy-production floor under bridge assumptions.

Dependency

Landauer bridge; correction channels

Failure

Logically irreversible erature violates Landauer lower bound under stated assumptions.

Consequence

Demote Landauer floor claim.

P5-005

Housekeeping entropy persists even when logical erasure is zero.

Dependency

Reversible embedding; carrier maintenance

Failure

Boundary maintenance, refresh, clocking, sensing, and repair cost-free when erasure is zero.

Consequence

Demote housekeeping claim.

P5-006

Externalization shifts rather than removes the entropy ledger.

Dependency

Accounting boundary; externalization audit

Failure

External records impose no write, verification, retrieval, sync, or maintenance cost.

Consequence

Revise externalization claim.

P5-007

Pruning and invariant compression can reduce future entropy-production pressure.

Dependency

T3 Phase-B invariants; pruning ROI model

Failure

No task-preserving simplification ever reduces refresh, repair, or verification cost.

Consequence

Demote pruning-relief claim.

P5-008

Deficit crossing predicts measurable signatures in heat, resource use, latency, resets, or error floor.

Dependency

Deficit-crossing protocol; ledger decomposition

Failure

Positive deficit sustained with no measurable change in any physical or task channel.

Consequence

Demote deficit-signature claim.

T2-001

Finite observers have bounded distinguishability budgets.

Dependency

FDS-T1

Failure

A finite physical observer reliably registers, preserves, and updates unlimited distinctions with finite resources.

Consequence

Demote T2 claim; T1 bridge survives.

T2-002

Horizons act as causal-access boundaries.

Dependency

General relativity

Failure

Local causal horizons are irrelevant to observable access, entropy, or thermodynamic accounting.

Consequence

Demote T2 claim; core physics unchanged.

Operational Claims

Passive mappers do not qualify as strong FDS-agents.

Dependency

Boundary, update, resource, and persistence criteria

Failure

Update ablation does not affect future boundary-maintenance loss.

Consequence

Revise AI agency criterion.

A1-D

Strong FDS-agency requires resource-governed persistence.

Dependency

FDS tuple + persistence test

Failure

System satisfies task output competence without durable update or boundary maintenance.

Consequence

Classify as mapper/scaffold, not strong agent.

A1-C

FDS-agency requires action-to-future-state causal influence.

Dependency

Intervention / transfer influence test

Failure

Actions have no measurable influence on future boundary-relevant states.

Consequence

Revise causal loop criterion.

A1-E

Capacity-deficit estimation is required to distinguish scaling from agency.

Dependency

Task demand + system capacity estimate

Failure

Systems qualify as agents without measurable boundary-relevant capacity pressure.

Consequence

Revise capacity-deficit criterion.

Domain Bridge Claims

B1-1

Immune systems can be modeled as finite-capacity boundary-verification architectures.

Dependency

B0 biomedical bridge governance; FDS core capacity definitions

Failure

Immune response can be fully organized without finite classification, memory, resource, boundary, or verification roles.

Consequence

Demote B1-1.

B1-2

Immune action requires admission and classification of candidate distinctions before downstream response.

Dependency

B1-1; recognition-admission-verification-action pipeline

Failure

Action is empirically independent of admission, classification, memory, or context in the specified model.

Consequence

Revise B1-2.

B1-3

Immune classification is better modeled as a boundary-state vector than as a single self/non-self label.

Dependency

B1-1; multiaxis classification

Failure

A one-dimensional label captures all relevant verification behavior in the declared system.

Consequence

Revise B1-3.

B1-4

High candidate-distinction load should produce delay, broad default action, reduced specificity, false positives/negatives, or FDS-resolution failure.

Dependency

B1-1; verification saturation; VLR control number

Failure

Increasing verification burden produces no change in accuracy, delay, alarm load, resource use, or resolution.

Consequence

Demote B1-4.

B1-5

Immune memory reduces future verification cost but can produce drift, overgeneralization, or tolerance risk.

Dependency

B1-1; memory-tolerance tradeoff

Failure

Memory has no measurable cost, drift, or threshold effect in the declared system.

Consequence

Revise B1-5.

B1-6

Some perturbations actively consume verification capacity or modify classification (adversarial sabotage).

Dependency

B1-1; adversarial distinction injection model

Failure

Evasion-like processes never alter Y, pi, M, Phi, or C_verify in declared models.

Consequence

Demote B1-6.

B1-7

Immune verification is constrained by routing, migration, amplification, and return times (distributed spatial latency).

Dependency

B1-1; spatial latency graph model; SLR control number

Failure

Spatial latency has no measurable effect in systems where local damage timescale is shorter than verification time.

Consequence

Revise B1-7.

Self-organization as boundary maintenance under finite capacity.

Dependency

FDS core definitions; finite capacity; budget exits

Failure

Freezing internal update has no effect on future boundary loss.

Consequence

Demote self-organization bridge.

N1-001

Active self-organization requires boundary-maintenance-relevant internal update.

Dependency

Active boundary criterion; finite capacity

Failure

System classified active even when update ablation has no effect on future boundary loss.

Consequence

Revise active self-organization definition.

N1-002

Effective organizational capacity is task-relative and reduced by coordination, verification, latency, resource, and externalization costs.

Dependency

Finite capacity; bottleneck logic

Failure

Boundary tasks maintained at full fidelity when all capacity factors fall below demand.

Consequence

Revise organizational capacity model.

N1-003

Capacity deficit creates maintenance-load pressure, not necessarily raw complexity growth alone.

Dependency

Capacity deficit; maintenance load equation

Failure

Increasing task demand never increases maintained load in any implementation.

Consequence

Demote deficit-pressure claim.

N1-004

Unbounded Phase-A growth is impossible under finite resource input without exit channels.

Dependency

Finite resource envelope; exit channel taxonomy

Failure

Active finite systems grow maintained load forever under finite resources with no exit.

Consequence

Revise exit theorem.

N1-005

Pruning has a viability window and is resource-gated.

Dependency

Resource-gated pruning equation

Failure

Pruning strength has no systematic effect on overload or persistence across controlled cases.

Consequence

Demote pruning model.

N1-006

Externalization shifts rather than removes boundary-maintenance burden, and can clog the environment.

Dependency

Accounting boundary; externalization ROI equation

Failure

External records impose no storage, verification, retrieval, or repair burden in any implementation.

Consequence

Revise externalization model.

N1-007

Phase-C catastrophic feedback couples boundary loss with resource depletion.

Dependency

Resource and loss dynamics; positive loop gain

Failure

Resource depletion and boundary loss never couple positively in collapse-prone systems.

Consequence

Demote Phase-C collapse regime.

N1-008

Phase-B residues are biased toward low-maintenance, task-relevant invariants.

Dependency

T3 Phase-B invariants; survival score function

Failure

Residues after overload show no bias toward reduced maintenance cost or task relevance.

Consequence

Demote invariant-bias claim.

Organizations and civilizations can be modeled as active finite distinction systems.

Dependency

Institutional boundary + memory + resource budget

Failure

Persistent institutions avoid collapse under unlimited complexity growth without pruning, externalization, or reform.

Consequence

Demote civilization bridge.

High-Risk Claims

Show high-risk registry notes (1 claims)

High-risk bridge hypothesis: horizon-maintenance dark energy under finite distinguishability budgets.

Dependency

Cosmological bridge assumptions

Failure

Observations force exact Lambda behavior beyond stated tolerance.

Consequence

Demote X1.