Pith Number

pith:YXGAUVKQ

pith:2025:YXGAUVKQAKUIZ74EIINMA5OTQO

not attested not anchored not stored refs pending

Gap metrics for stationary point processes and quantitative convexity of the free energy

Bastian M\"uller, Martin Huesmann

arxiv:2509.08659 v1 · 2025-09-10 · math.PR

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{YXGAUVKQAKUIZ74EIINMA5OTQO}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more · Embed verified badge

Record completeness

1 Bitcoin timestamp

2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

✓ Portable graph bundle live · download bundle · merged state

The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Receipt and verification

First computed	2026-07-05T12:08:33.812776Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c5cc0a555002a88cff84421ac075d3838f9d10e71e3833391e9600d3284e6d63

Aliases

arxiv: 2509.08659 · arxiv_version: 2509.08659v1 · doi: 10.48550/arxiv.2509.08659 · pith_short_12: YXGAUVKQAKUI · pith_short_16: YXGAUVKQAKUIZ74E · pith_short_8: YXGAUVKQ

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/YXGAUVKQAKUIZ74EIINMA5OTQO \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: c5cc0a555002a88cff84421ac075d3838f9d10e71e3833391e9600d3284e6d63

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1c654fd40f94ced4cce1fad272a6deeff966f8d0a566f1db083dd87e70bbd559",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2025-09-10T14:53:47Z",
    "title_canon_sha256": "65fba32f20dde95547bf3d3f36b18d5eae05edf432530b8f47bb01726f8d57cf"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2509.08659",
    "kind": "arxiv",
    "version": 1
  }
}