feat(M13.1): add CAT/EPT scale-dilation soliton tensor model

[jagg-ix]

M13.1

Introduces a new CAT/EPT model lineage for the exact multiplicative scale geometry underlying entropic proper distance, then transports the existing M11 pointwise soliton and finite-cutoff infinite-mode Liouville tensor across that scale line.

Scale group and Noether mechanics

The executable campaign checks:

• the dilation flow lambda(t) = exp(H t) identity, composition and inverse laws;
• invariance of L(lambda, lambda_dot) = 1/2 (lambda_dot/lambda)^2 under common dilation;
• the Euler–Lagrange identity lambda_ddot lambda = lambda_dot^2;
• conservation of the Noether charge Q = lambda_dot/lambda = H;
• the exact log-coordinate representation of the flow.

Invariant scale metric

It implements d(x,y) = |log(x/y)|, checking common-dilation isometry and exact transport to additive log coordinates. Entropic proper distance is represented as r = lambda_C log K, with exponential recovery of the supplied Schmidt number.

Lattice ladder and half-step

• block-spin scales a_n = 2^n a_0 have equal step length log 2;
• the total distance to rung n is exactly n log 2;
• the continuous path 2^r is a geodesic in the scale metric;
• sqrt(2) lies exactly one half blocking step from unity.

Entropic and gauge-sector orbits

• the entropic-horizon energy law is verified as the dilation orbit with generator H = -2;
• the zero-charge SU(2) abelian Gauss sector is fixed under the flow;
• a charged sector moves through the scale metric at speed |q|.

Pointwise and infinite-mode particle carrier

M13 reuses, rather than duplicates:

• the M11.1 exact pointwise bright-soliton carrier;
• the M11.2 finite-cutoff realization of an infinite mode set with fixed finite particle number;
• the M12 particle-zoo registration and supplied charged-lepton mass data.

Across the scale rungs, the campaign verifies soliton normalization, stationary residuals, inverse scale-width transport, scale-metric spacing, and Liouville trace, Hermiticity, positivity, purity and retained-probability bounds.

Formal and ZIL authority

The ledger pins jagg-ix/entropic-physlib-private, branch entropic-physlib-linear-full, TIP 8bafa9ab93cbb39e85909fc3837bb4b6e0dec748, including:

• ScaleDilationLogMetric.lean@0c8262ba;
• EntropicProperDistance.lean@6ea714cb;
• ComplexNoetherChargeEntropicHorizon.lean@79c6994c;
• LiouvilleSecondQuantization.lean@9d2c905c.

The ZIL graph records the dependencies and exclusions explicitly.

Claim boundary

This PR does not claim:

• first-principles particle masses, charges or couplings;
• a completed infinite-particle Fock Hilbert space;
• new lattice simulation data;
• a complete AdS/CFT or holographic dictionary.

M12 masses are supplied labels. The QCD ladder and holographic radial coordinate are scale-geometry interpretations of exact formal identities.

Validation

Validated before publication:

• all M13 Python modules compiled;
• the formal JSON ledger parsed;
• the focused M13 test passed;
• all 8 top-level M13 acceptance groups passed;
• the reused M11 and M12 studies passed;
• every remote file blob matches the locally validated file exactly.

No repository CI workflow was added or modified.

Branch audit

• base: main@eb98afe82a6928a7e9247b60829c55a88193b670
• head: 5d69fe43e76d3e2aa23d1ef8309902ed06fbd2dd
• one isolated M13.1 commit
• 10 changed files
• one commit ahead, zero behind
• GitHub mergeability: clean

[jagg-ix]

Final M13.1 audit:

• base main@eb98afe82a6928a7e9247b60829c55a88193b670
• head 5d69fe43e76d3e2aa23d1ef8309902ed06fbd2dd
• one commit ahead, zero behind
• 10 isolated M13 files
• GitHub mergeability: clean
• every remote file blob matches the locally validated file exactly
• Python compilation passed
• formal JSON ledger parsed
• focused M13 test passed (1 passed)
• no workflow file was added or modified

Formal TIP: entropic-physlib-linear-full@8bafa9ab93cbb39e85909fc3837bb4b6e0dec748; principal source ScaleDilationLogMetric.lean@0c8262bac90d2dff03a04cc8e15efb21ee87ff0e.