UNNS SUBSTRATE RESEARCH PROGRAMunns.tech
STRUCTURAL ACCESSIBILITY · SPECTRAL DISCRETENESS
Structural Accessibility and
Spectral Discreteness in Pure SU(3) Yang–Mills
UNNS REASSESSMENT OF VACUUM NON-CROSSABILITY AND THE MASS GAP
Empirical Coexistence  ·  Structural–Spectral Separation Theorem  ·  Open Π Problem  ·  Frozen Verdict Register
FROZEN EVIDENCE CHAIN UNNS_YM_GAP → UNNS_VACUUM_CONTINUITY · arrows are logical, not causal Non-crossability program (UNNS_YM_GAP) Δ_struct ≥ δ > 0 under refinement; Class B crosses 0 at β=6.71 NOT ESTABLISHED Structural vacuum accessibility (5 representations) no universal positive exclusion floor detected · H_acc^emp SUPPORTED Independent spectral positivity M/√σ = 3.405(21) · r0·M = 4.16(11)(4) · own coordinates POSITIVE ×2 BRIDGE-III coexistence (deterministic evaluator) frozen statuses only · empirical, within the frozen architecture COEXISTENCE-SUPPORTED empirical accessibility is supported; the limit statement H_acc^lim is not established SEPARATION THEOREM (ELEMENTARY) a gap does not by itself imply a structural exclusion neighborhood (a) — Counterexample gap > 0 with S = {0} ∪ {1/n}: structural convergence without spectral convergence (b) — Continuity is sufficient continuity of ε at V ⇒ exclusion neighborhood; not necessary (c) — Accessibility ⇒ discontinuity X_n → V with a persistent gap ⇒ oscillation of ε at V ≥ Δ (d) — Factorization ε = E∘Π one of Π continuous at V / E continuous at Ω must fail (e) — Hölder bridge ε ≤ C·d^α ⇒ exclusion radius δ = min{r, (Δ/C)^(1/α)} premise not empirically instantiated · no Clay claim
Structural proximity is not spectral proximity.   A positive gap constrains energies, not structure; they are linked only by a bridge — sufficient when it holds, and ruled out by accessibility under a persistent gap.
MANUSCRIPT FROZEN · v3 · 42 PP H_acc^emp — SUPPORTED H_acc^lim — NOT ESTABLISHED H_iso — NOT ESTABLISHED THEOREM 1 (a)–(e) · ELEMENTARY Π: S_UNNS → Y_spec — OPEN COEXISTENCE: EMPIRICAL, FROZEN ARCHITECTURE NO CLAY CLAIM · Oct 2026
Manuscript · PDF
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Structural Accessibility and
Spectral Discreteness
The unified manuscript of both projects. Separates four notions of nearness, reports the original non-crossability program in full, tests structural vacuum accessibility across five representations, adds independent spectral positivity, and proves the structural–spectral separation theorem with the open Π problem stated at its own level.
UNNS Substrate Research Program · 42 pages · 29+ references · Oct 2026
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Analytics · HTML
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UNNS Vacuum Continuity
Research Analytics
Interactive reproducibility instrument built from the frozen records of UNNS_YM_GAP and UNNS_VACUUM_CONTINUITY: verdict strings audited against source, SHA-256 provenance, the Class B margin and AICc evidence, the spectral anchors, and the BRIDGE-III evaluation.
generated from frozen project records · claim–evidence mapping
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Data & Corpus · GitHub
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Data and Corpus
Construction
The UNNS_YM_STRUCTURAL_SPECTRAL project folder: the corpus and records on which the manuscript rests, pinned to a fixed commit so the cited repository state is reproducible.
commit aa17dbc9 · projects/UNNS_YM_STRUCTURAL_SPECTRAL
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5STRUCTURAL REPRESENTATIONS
3.405(21)M(0++)/√σ · AT20
4.16(11)(4)r0·M(0++) · CHEN ET AL.
−0.0034S_B AT β=6.71 (CROSSING)
-0.03+0.00+0.03+0.06β=6.2+0.0204β=6.4+0.0359β=6.71-0.0034β=6.93+0.0519S_B = log10(R_p=8 / R_B) · 95% INTERVALSdashed line = proposed boundary S_B = 0 · only β=6.71 is sign-unstable → DATA-INDETERMINATE
First project, turning point. Class B margins stay positive at three of four ensembles; the central value at β=6.71 is negative but its preregistered interval straddles zero, so the verdict is DATA-INDETERMINATE, neither falsification nor persistence.
0123400.10.20.30.4continuum anchor 3.405(21)M(0++)/√σ vs a√σ · AT20 LADDERindependent anchor (own coordinate, not converted): r0·M(0++) = 4.16(11)(4) · both strictly positive
Independent spectral positivity. Lattice points are not continuum-extrapolated; they only show the approach to the anchor. The two spectral scales use different coordinates and are deliberately not converted into one another.
ΔAICc = AICc(floor) − AICc(zero) · POSITIVE FAVORS ZERO02468decisive = 6CEA primary / exponentialCEA primary / K0CEA drop-first / exponentialCEA drop-first / K0EMT R=0.46 primary / K0EMT R=0.46 primary / expEMT R=0.46 drop-first / K0EMT R=0.46 drop-first / expEMT R=0.69 primary / K0EMT R=0.69 primary / expEMT R=0.69 drop-first / K0EMT R=0.69 drop-first / expEMT R=0.92 primary / K0EMT R=0.92 primary / expEMT R=0.92 drop-first / K0EMT R=0.92 drop-first / exp
Zero floor vs positive floor. Positive values favor the zero floor. Only the CEA drop-first sensitivity crosses the frozen decisive threshold of 6; all twelve EMT values lie in 0.82–2.09, so the EMT branch stays EMT-UNCERTAINTY-LIMITED and no verdict is promoted.
FROZEN VERDICT REGISTER
G9UNNS_YM_GAP closureNOT ESTABLISHED
G7YM-3B Class B (β=6.71 crossing)DATA-INDETERMINATE
G6YM-3A Class C, 8 levelsMODEL-REFINEMENT PERSISTENT
V1Baker 2022 · VREF-I/ACALIBRATION-SENSITIVE
V2Cea 2017 · VREF-I/BREFINEMENT-INDETERMINATE
V3Cea · STRUC-I / STRUC-PERC-IARCHITECTURE-PRESERVED
V4Battelli–Bonati 2019 controlUNSMOOTHED-ARCHITECTURE-CONSISTENT
V5Yanagihara 2019 · EMT-I R=0.69 fmEMT-UNCERTAINTY-LIMITED
V6EMT geometry R=0.46, 0.92 fmGEOMETRY-ROBUST-NO-FLOOR
V7Stage 2 synthesisNO-UNIVERSAL-STRUCTURAL-EXCLUSION-DETECTED
V8Stage 2 interpretationSTRUCTURAL-VACUUM-ACCESSIBILITY-SUPPORTED
V9SPEC-I/A · AT20SPECTRAL-SCALE-POSITIVE
V10SPEC-I/B · Chen et al.SPECTRAL-SCALE-POSITIVE
V11BRIDGE-IIICOEXISTENCE-SUPPORTED
V12Project levelSTRUCTURAL-SPECTRAL-COEXISTENCE-SUPPORTED
ESTABLISHED · EMPIRICAL
Structural accessibility (H_acc^emp) is supported and coexists with two independent positive continuum scalar scales in the tested pure-SU(3) representations.
PROVED · ELEMENTARY THEOREM
A gap alone does not imply structural exclusion. Continuity, or a local Hölder upper bound, is a sufficient bridge; accessibility plus a persistent gap rules out a continuous bridge.
OPEN · UNNS PROBLEM
Construct Π: S_UNNS → Y_spec and determine its topology; establish H_acc^lim rather than only H_acc^emp.
NOT CLAIMED
V ∈ closure(A_YM \ {V}); the limit statement; a Clay mass-gap theorem; a derivation of the gap from UNNS structure.
FOUR NOTIONS OF NEARNESS
CONFIGURATION & OBSERVABLE SPACE
Stage 2 lives in observable space: vacuum-subtracted profiles, tails and the EMT norm. No representation-independent metric on configurations was constructed.
HILBERT-SPACE & SPECTRAL NEARNESS
Norm convergence to the vacuum ray can coexist with a fixed support edge. The gap acts only on the final energy axis; Stage 3 lives there.
“Theorem 1 establishes that structural convergence need not imply spectral convergence. The empirical results are compatible with this architecture and support structural accessibility, but do not establish the limiting sequence required to instantiate the theorem in Yang–Mills.”
ORIGINAL PICTURE: NOT ESTABLISHED, NOT REFUTED STAGE 2 STATES = PROFILE WINDOWS, NOT EXCITATIONS NO UNIVERSAL FLOOR DETECTED · TESTED REPRESENTATIONS
unns.tech  ·  UNNS Substrate Research Program  ·  2026