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# AK‑HDPST v15.0 — Release Notes

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@Kobayashi2501 Kobayashi2501 released this 05 Sep 00:03
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AK‑HDPST v15.0 — Release Notes

Tag: v15.0
Date: 2025‑09‑05

Two‑layer, auditable proof framework for functorial collapse via higher‑dimensional projections and controlled obstruction removal.

  • Core: machine‑checkable statements in 1D constructible persistence over a field
  • [Spec]: safe extensions under explicit, auditable hypotheses, non‑expansive after truncation

Highlights

  • Exact truncation T_tau (Serre reflector) formalized as the single source of strong claims
  • Windowed protocol standardized: t -> persistence -> T_tau -> compare
  • B‑Gate+ (collapse gate) with safety margin and delta‑ledger, per window
  • Tower diagnostics (mu, nu) with stability bands and window pasting (Restart + Summability)
  • Spec pipeline made auditable and composable:
    • Mirror/Tropical with quantitative commutation and additive pipeline budget
    • Soft‑commuting A/B policy for multi‑axis exact reflectors
    • Lax monoidal tensor/collapse with windowed energy bounds
    • PF/BC transported to persistence with window protocol
    • Fukaya realization with action filtration and permitted‑operations table
  • Reproducibility: versioned artifacts (bars/spec/ext/phi), cross‑linked hashes, run.yaml schema
  • Formalization stubs (Lean/Coq) for reflectors, diagnostics, gate, PF/BC, and budget API

What’s New

Core (provable)

  • Exact, idempotent, 1‑Lipschitz T_tau deletes all bars with length <= tau
  • Filtered lift C_tau up to f.q.i. with P_i(C_tau F) ~ T_tau(P_i F)
  • One‑way bridge only: PH1(F)=0 => Ext1(R(F), k)=0 under t‑exact realization with amplitude <= 1
  • Tower diagnostics (mu, nu):
    • Subadditivity under composition
    • Additivity under finite sums
    • Cofinal invariance
    • Stability‑band detection via tau‑sweep
  • Windowed pasting:
    • B‑Gate+ per window (PH1=0, Ext1=0 if applicable, mu=nu=0, gap_tau > sum(delta))
    • Restart inequality + Summability to paste window certificates globally

[Spec] (audited, non‑expansive after truncation)

  • Mirror/Tropical quantitative commutation:
    • Natural 2‑cell Mirror C_tau => C_tau Mirror with uniform delta(i, tau)
    • Pipeline budget is additive, uniform in the input, non‑increasing under 1‑Lipschitz post‑processing
  • Multi‑axis exact reflectors:
    • Order independence for nested torsions
    • A/B soft‑commuting policy with tolerance, fallback order, and delta_alg logging
  • Lax monoidal compatibility:
    • Windowed energy upper bounds via overlap integrals
    • Monomorphy regime (M3+) gives post‑collapse dominance
  • Projection Formula / Base Change:
    • Transported to persistence via the windowed protocol
    • Any numeric drift after truncation is logged as delta (disc/meas)
  • Fukaya realization:
    • Continuation is 1‑Lipschitz; stop addition/sector shrinking are deletion‑type
    • Permitted‑operations table mapping ops -> delta‑ledger -> B‑Gate+

Breaking Changes

  • Gate usage consolidated into B‑Gate+ (per window) with safety margin and delta‑ledger; legacy ad‑hoc gates are deprecated
  • All comparisons must follow the windowed protocol:
    • for each window: t -> persistence -> T_tau -> compare
  • Ext tests are only used in the one‑way direction and only under t‑exact, amplitude <= 1
  • Spec steps must be non‑expansive after truncation and must log delta in the ledger

Upgrade Guide (v14.x -> v15.0)

  1. Adopt the window protocol in your pipelines:
  • Replace earlier direct comparisons with: t -> persistence -> T_tau -> compare
  1. Switch to B‑Gate+:
  • Add per‑window gap_tau and sum_delta checks
  • Enforce mu=nu=0 after truncation for tower diagnostics
  1. Add a delta‑ledger in your run.yaml:
  • Record delta_alg (algorithmic), delta_disc (discretization), delta_meas (measurement)
  • For Mirror/Transfer, record delta(i, tau); for non‑nested reflectors, record Delta_comm from A/B tests
  1. Migrate Ext usage:
  • Only one‑way bridge; add t_exact: true, amplitude_leq_1: true flags in gate checks
  1. Adopt Spec contracts:
  • Mirror/Tropical: add delta_budget, hypotheses
  • PF/BC: ensure window protocol and proper/smooth hypotheses are documented

Minimal run.yaml diff

 windows:
-  - [0.0, 1.0]
+  - label: w0
+    range: [0.0, 0.5)
+  - label: w1
+    range: [0.5, 1.0)

 truncation:
-  tau: 0.1
+  tau: 0.15
+  lift: C_tau
+  reflector: T_tau

 gate:
-  ext1: true
+  require:
+    PH1_zero: true
+    Ext1_zero: true      # only if t-exact & amplitude <= 1
+    mu_zero: true
+    nu_zero: true
+    gap_tau_gt_sum_delta: true

 audit:
-  outputs: ["bars"]
+  outputs: ["bars","spec","ext","phi"]
+  checksums: "sha256"

 spec:
+  enabled: true
+  items:
+    - name: mirror_transfer
+      hypotheses: ["nonexpansive_after_truncation","delta_controlled_commutation"]
+      delta_budget: 0.01

Compatibility

  • Persistence backends: any 1D constructible persistence implementation
  • Python: 3.9+
  • Optional: Lean 4 / Coq (for formalization stubs)
  • OS: Linux / macOS / Windows (WSL recommended for large runs)

Install

git clone https://github.com/your-org/ak-hdpst.git
cd ak-hdpst
python -m venv .venv
source .venv/bin/activate
pip install -e ".[all]"

Quickstart

# Copy an example config
cp examples/minimal/run.yaml ./run.yaml

# Run
akhdpst run run.yaml

# Audit (windowed)
akhdpst audit out/artifacts --by-window

# Check B-Gate+ (window w0)
akhdpst gate check --run run.yaml --window w0

Python:

from akhdpst.core import T_tau, C_tau
from akhdpst.gate import collapse_admissible
from akhdpst.audit import audit_tower

F = ...  # load filtered complex
tau = 0.15
F_tau = C_tau(F, tau)
ok = collapse_admissible(F, realization="Db(k-mod)", t_exact=True, amplitude_leq_1=True)
mu, nu = audit_tower([F0, F1, F_inf], tau)

Examples

  • examples/windowed: Window protocol, B‑Gate+, tower diagnostics
  • examples/spec/mirror: Mirror/Transfer with delta control and pipeline budget
  • examples/pfbc: Projection formula/base change audit via window protocol
  • examples/fukaya: Action‑filtered realization and permitted op table

Known Issues

  • Spectral indicators are not invariants up to f.q.i.; use fixed policy (beta, M(tau), s) for comparisons
  • No global equivalence PH1 <-> Ext1 is claimed; the bridge is one‑way only
  • Type IV (limit failures) require proper tau selection; use tau‑sweep and stability bands

Changelog (selected)

  • Core
    • Formalized T_tau and C_tau relationship; tightened Lipschitz scope
    • Tower calculus: subadditivity, additivity, cofinal invariance; stability bands; pasting
  • Spec
    • Mirror/Tropical: quantitative commutation, additive delta budget
    • Reflectors: A/B soft‑commuting policy, fallback with delta_alg
    • Lax monoidal: windowed energy bounds; monomorphy regime (M3+)
    • PF/BC: transported to persistence with windowed protocol
    • Fukaya: action filtration; permitted operations; delta‑ledger integration
  • Tooling
    • run.yaml schema extended (windows, truncation, spec items, gate, audit)
    • Artifacts bars/spec/ext/phi with checksums and audit summaries
    • CLI and Python API for gate, audit, diagnostics

Contributing

  • Keep Core vs [Spec] separation explicit in code and docs
  • Add Spec items only with non‑expansive‑after‑truncation checks and delta‑ledger entries
  • Include examples and tests; update examples/ and tests/

Dev quickstart:

pip install -e ".[dev]"
pytest -q
ruff check .
mypy akhdpst

License

MIT License. See LICENSE.

Citation

AK–HDPST v15.0: Exact Truncation, Collapse Gate, and Auditable Spec Extensions
Authors: ...
Year: 2025
URL: https://github.com/your-org/ak-hdpst

References

  • W. Crawley‑Boevey (2015). Decomposition of pointwise finite‑dimensional persistence modules.
  • F. Chazal, V. de Silva, S. Glisse, S. Oudot (2016). Structure and stability of persistence modules and barcodes.
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