Skip to main content

CIndex

Claim ID index

102 unique claim IDs, including 55 ULR-* IDs, extracted from the public corpus. This is a lexical navigation index: canonical, active, historical, and retracted status remains owned by each linked ledger.

C

  • C-0001
    Claim C-0001 — The Soft Cohesion Field is Primitive

    … uished regions where $u$ is high, stable, and temporally persistent. > **ID:** C-0001 · **Status:** validated · **Confidence:** 100% · **Proposed:** 2026-03-26 > **E …

    SCC archive · +3 more

  • C-0002
    Claim C-0001 — The Soft Cohesion Field is Primitive

    … "crisp object" — that remains a downstream question --- ## Related Claims - C-0002: Objects are distinguished formations (not primitives) - C-0003: Formations are …

    SCC archive · +2 more

  • C-0003
    Claim C-0001 — The Soft Cohesion Field is Primitive

    … lated Claims - C-0002: Objects are distinguished formations (not primitives) - C-0003: Formations are defined by proto-cohesion (Bind ∧ Sep ∧ Artic ∧ Persist) --- …

    SCC archive · +2 more

  • C-0004
    Claim C-0002 — The K-Field Architecture is Necessary

    … itive - C-0003: K=2 exists as kinetically-trapped metastable state (Option C) - C-0004: Repulsion prevents formation coalescence [TBD] --- ## Validation Status | C …

    SCC archive

  • C-0007
    T7-Enhanced — Non-Idempotent Metastability Advantage

    > **Hero · Phase + Stability group · Cat A.** > Source: C-0007 / P-0007. Verification: E-0008, E-0009 (residence time, $p = 0.037$). > Canonic …

    SCC archive · +1 more

  • C-0008
    T8-Core — Phase Transition (Spectral Universality)

    > **Hero · Phase + Stability group · Cat A.** > Source: C-0008 / P-0008. Verification: E-0010, E-0011. Canonical version: CV-1.0. > Full state …

    SCC archive · +1 more

  • C-0009
    SCC Theorem Registry

    … ear at critical β | | **T-8-Full** | Phase Transition (Global) | accepted | A | C-0009 | P-0009 | E-0012, E-0013 | Full energy landscape bifurcation | | **T-11** | Γ- …

    SCC archive

  • C-0011
    T11 — Sharp-Interface Γ-Convergence

    > **Hero · Phase + Stability group · Cat A.** > Source: C-0011 / P-0011. Verification: E-0014. Canonical version: CV-1.0. > Full proof: [Canon …

    SCC archive · +1 more

  • C-0014
    T14 — Gradient Flow Convergence (Łojasiewicz)

    > **Hero · W4 Capstone group · Cat A.** > Source: C-0014 / P-0014. Verification: E-0020:E-0022. Canonical version: CV-1.0. > Full proof: …

    SCC archive · +1 more

  • C-0020
    T20 — Axiom Consistency (A1' resolves A1↔A3 incompatibility)

    > **Hero · Foundation group · Cat A.** > Source: C-0020 / P-0020. Verification: E-0025. Canonical version: CV-1.0. > Full statement and …

    SCC archive · +1 more

  • C-0101
    SCC Theorem Registry

    … y consistent | | **C-Axioms** | Cohomology-Resolvent Alignment | accepted | A | C-0101 | P-0101 | E-0030:E-0032 | C3'' symmetrization complete (upgraded 04-03) | | ** …

    SCC archive

  • C-0110
    SCC Theorem Registry

    … 04-03) | | **QM-1** | Quantum Mechanical Analogy (Eigenvalue) | accepted | A | C-0110 | P-0110 | E-0040 | Fiedler eigenvalue is binding edge | | **QM-2** | QM-2 (Spe …

    SCC archive

  • C-0111
    SCC Theorem Registry

    … eigenvalue is binding edge | | **QM-2** | QM-2 (Spectral Gap) | accepted | A | C-0111 | P-0111 | E-0041 | Spectral gap related to phase transition | | **QM-3** | QM- …

    SCC archive

  • C-0112
    SCC Theorem Registry

    … related to phase transition | | **QM-3** | QM-3 (Perturbation) | accepted | A | C-0112 | P-0112 | E-0042 | Perturbations stay confined | | **QM-4** | QM-4 (Commutatio …

    SCC archive

  • C-0113
    SCC Theorem Registry

    … Perturbations stay confined | | **QM-4** | QM-4 (Commutation) | accepted | A | C-0113 | P-0113 | E-0043 | Operator commutation holds generically | | **T-Bind-Proj** …

    SCC archive

  • C-0200
    SCC Theorem Registry

    … esidual Bound at Constrained Minimizers | accepted | A (for all τ_cl ∈ (0,1)) | C-0200 | P-0200 | E-0050:E-0052 | Tangential Residual Bound at Constrained Minimizers; …

    SCC archive

  • C-0201
    SCC Theorem Registry

    … | **T-Bind-Full** | Bind Lower Bound at Constrained Minimizers | accepted | A | C-0201 | P-0201 | E-0053 | Bind Lower Bound at Constrained Minimizers; $\mathsf{Bind}( …

    SCC archive

  • C-0300
    SCC Theorem Registry

    … | **Predicate-Energy Bridge** | Energy ↔ Diagnostic Alignment | accepted | A | C-0300 | P-0300 | E-0060:E-0063 | Energy minimization ↔ diagonal optimization (upgrade …

    SCC archive

  • C-0301
    SCC Theorem Registry

    … pgraded 04-03) | | **Deep Core Dom. 2b** | Deep Core Dominance | accepted | A | C-0301 | P-0301 | E-0064, E-0065 | Core is always dominant in asymmetric regime (upgra …

    SCC archive

  • C-0400
    SCC Theorem Registry

    … d 04-03) | | **T-Persist-1(a)** | Transport Persistence (base) | accepted | C | C-0400 | P-0400 | E-0070 | Conditional: assumes generic parameters | | **T-Persist-1(b …

    SCC archive

  • C-0401
    SCC Theorem Registry

    … T-Persist-1(b)** | Transport Persistence (basin unconditional) | accepted | A | C-0401 | P-0401 | E-0071, E-0072 | Unconditional: genericity automatic (upgraded 04-03 …

    SCC archive

  • C-0402
    SCC Theorem Registry

    … | | **T-Persist-1(d)** | Transport Persistence (fixed stratum) | accepted | C | C-0402 | P-0402 | E-0073 | Conditional: on fixed active stratum | | **T-Persist-1(e)** …

    SCC archive

  • C-0403
    SCC Theorem Registry

    … m | | **T-Persist-1(e)** | Transport Persistence (confinement) | accepted | A | C-0403 | P-0403 | E-0074 | Tight confinement bound (upgraded 04-03) | | **T-Persist-Fu …

    SCC archive

  • C-0404
    SCC Theorem Registry

    … **T-Persist-Full** | Transport Persistence (full composition) | accepted | C | C-0404 | P-0404 | E-0075 | Conditional on multiple regime conditions | | **T-Persist-K …

    SCC archive

  • C-0500
    SCC Theorem Registry

    … | | **T-Persist-K-Sep** | K-field Persistence (well-separated) | accepted | C | C-0500 | P-0500 | E-0076, E-0077 | Conditional: on well-separated regime + per-formati …

    SCC archive

  • C-0501
    SCC Theorem Registry

    … | | **T-Persist-K-Weak** | K-field Persistence (weak coupling) | accepted | C | C-0501 | P-0501 | E-0078 | Conditional: on weakly-interacting regime | | **T-Persist-K …

    SCC archive

  • C-0502
    SCC Theorem Registry

    … | | **T-Persist-K-Unified** | K-field Persistence (parametric) | accepted | C | C-0502 | P-0502 | E-0046, E-0047 | Parametric family (Sep/Weak/Strong); 100% validatio …

    SCC archive

  • C-0550
    SCC Theorem Registry

    … A lemma (Lemma 4), 1 Cat A corollary (F-1 split-resolution). - Status changes: C-0550 (F-1), C-0551 (M-1), C-0552 (MO-1) — challenged → resolved/clarified/sidesteppe …

    SCC archive

  • C-0551
    SCC Theorem Registry

    … a 4), 1 Cat A corollary (F-1 split-resolution). - Status changes: C-0550 (F-1), C-0551 (M-1), C-0552 (MO-1) — challenged → resolved/clarified/sidestepped. - Counts: 3 …

    SCC archive

  • C-0552
    SCC Theorem Registry

    … corollary (F-1 split-resolution). - Status changes: C-0550 (F-1), C-0551 (M-1), C-0552 (MO-1) — challenged → resolved/clarified/sidestepped. - Counts: 35A → **37A**, …

    SCC archive

  • C-0553
    SCC Theorem Registry

    … corners). Multi-formation extension to $\Sigma^K_M$ still open (Phase 5). | | **C-0553** | Type A/B Classification | challenged | OP | exp65 | E-0065 | exp65 invalida …

    SCC archive

  • C-0600
    SCC Theorem Registry

    … allenged | OP | exp65 | E-0065 | exp65 invalidates; Type B never observed | | **C-0600** | K-field Model Selection | tentative (partially addressed) | pending | none …

    SCC archive

  • C-0700
    SCC Canonical Spec — Part 5: Proved Results Registry & Closing Notes

    … –experiment agreement), E-0091 (L=32 dichotomy). *Status:* **Proved**, Cat A. *(C-0700, P-0700.)* <Figure src="/content-assets/scc-figures/fig09-preobj-mechanism.p …

    SCC archive · +2 more

  • C-0701
    SCC Canonical Spec — Part 5: Proved Results Registry & Closing Notes

    … oretical and qualitative empirical confirmation. *Status:* **Proved**, Cat A. *(C-0701, P-0701.)* **Lemma 4. Quadratic Form Positive Definite (M matrix).** *(New, W4 …

    SCC archive · +2 more

  • C-0702
    SCC Canonical Spec — Part 5: Proved Results Registry & Closing Notes

    … > 0$) under the linear independence hypothesis. *Status:* **Proved**, Cat A. *(C-0702, P-0702.)* <Figure src="/content-assets/scc-figures/fig10-lemma4-quadratic-f …

    SCC archive · +2 more

  • C-0710
    SCC Canonical Spec — Part 5: Proved Results Registry & Closing Notes

    … ter mode-indexing artifact identified+resolved). *Status:* **Proved**, Cat A. *(C-0710, P-0710.)* <Figure src="/content-assets/scc-figures/fig11-goldstone-bloch.pn …

    SCC archive · +2 more

  • C-0711
    SCC Canonical Spec — Part 5: Proved Results Registry & Closing Notes

    … ntitative scaling carried as NQ-173 to W5+. Source: E-0096 (free BC partial). *(C-0711, P-0711.)* <Figure src="/content-assets/scc-figures/fig12-goldstone-nodal-co …

    SCC archive · +1 more

  • C-0712
    SCC Canonical Spec — Part 5: Proved Results Registry & Closing Notes

    … up $G_u$ acting unitarily on $T_{u^*} \Sigma_m$. *Status:* **Proved**, Cat A. *(C-0712, P-0712.)* **T-σ-Lemma-2. σ-Framework Nodal Count Properties.** *(New, W5 Day …

    SCC archive · +1 more

  • C-0713
    SCC Canonical Spec — Part 5: Proved Results Registry & Closing Notes

    … ntry. *Status:* **Proved (i)-(iv) Cat A**; (v)-(vi) **Cat C riders bundled**. *(C-0713, P-0713.)* **T-σ-Lemma-3. Goldstone–ℓ=1 Angular Saturation.** *(New, W5 Day 1 …

    SCC archive · +1 more

  • C-0714
    SCC Canonical Spec — Part 5: Proved Results Registry & Closing Notes

    … )* *Status:* **Proved Cat A in continuum**, discrete correction NQ-180 (W6+). *(C-0714, P-0714.)* **T-σ-Theorem-3. σ at Uniform on $D_4$ Free-BC Grid (Closed Form).* …

    SCC archive · +1 more

  • C-0715
    SCC Canonical Spec — Part 5: Proved Results Registry & Closing Notes

    … ty → single $E$; even pair → $A_1 \oplus B_1$.)* *Status:* **Proved**, Cat A. *(C-0715, P-0715.)* **T-σ-Theorem-4. σ at First Pitchfork on $D_4$ Free-BC Grid (Leadin …

    SCC archive · +1 more

  • C-0716
    SCC Canonical Spec — Part 5: Proved Results Registry & Closing Notes

    … -with-explicit-structural-parameter-5-theorems) for the row-level Cat B flag. *(C-0716, P-0716.)* #### W5 Day 3 EOD — D-6a Multi-Static Cluster (CV-1.5.1, 2026-04-29 …

    SCC archive · +1 more

  • C-0717
    SCC Theorem Registry

    … | Multi-Formation σ-Signature on K-field (Static) | accepted | A definitional | C-0717 | P-0717 | (theoretical extension of Commitment 14) | Defined on $\widetilde{\S …

    SCC archive

  • C-0718
    SCC Theorem Registry

    … Formation σ-Tuple Multi-Set Invariance | accepted | A (well-separated regime) | C-0718 | P-0718 | (theoretical via Coupling Bound Lemma + T-σ-Lemma-1) | Multi-set $\{ …

    SCC archive

  • C-0719
    SCC Theorem Registry

    … Static** | Between-Formation Cohomology Pull-Back | accepted | A definitional | C-0719 | P-0719 | (wreath-product representation theory, Specht 1935 + James-Kerber 19 …

    SCC archive

  • C-0720
    SCC Theorem Registry

    … -Formation Goldstone-Pair Instability (Phase 4 Static) | tentative | B target | C-0720 | (sketch) | (Phase 4 D-6a numerical, Phase 6 Q1 box-clipping) | Goldstone-pair …

    SCC archive

  • C-0721
    SCC Theorem Registry

    … ount Bridge under L1-J Regime | accepted | A (conditional under L1-J package) | C-0721 | P-0721 | (theoretical via L1-A..L1-L chain; numerical L1-I 439/1920 FEASIBLE_ …

    SCC archive

U