Pith Number

pith:WY4YTQTN

pith:2026:WY4YTQTNO5E4AZ5MPCIITNYH7S

not attested not anchored not stored refs pending

Path-Dependent Entropic Lagrangian for Probability Flows: Balance--Entropy Routing and Composable Information Potentials

Huilong Ren

arxiv:2607.10493 v1 · 2026-07-11 · math-ph · cs.IT · math.IT · math.MP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{WY4YTQTNO5E4AZ5MPCIITNYH7S}

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	2026-07-14T01:21:18.265814Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b63989c26d7749c067ac789089b707fc8a16733e212091a25824537de27179c8

Aliases

arxiv: 2607.10493 · arxiv_version: 2607.10493v1 · doi: 10.48550/arxiv.2607.10493 · pith_short_12: WY4YTQTNO5E4 · pith_short_16: WY4YTQTNO5E4AZ5M · pith_short_8: WY4YTQTN

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/WY4YTQTNO5E4AZ5MPCIITNYH7S \
  | 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: b63989c26d7749c067ac789089b707fc8a16733e212091a25824537de27179c8

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "850f4b4e34cbb50c77992d06592f851990e67a328b65bc5fb8fa09c2817e6e45",
    "cross_cats_sorted": [
      "cs.IT",
      "math.IT",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2026-07-11T21:58:07Z",
    "title_canon_sha256": "46731819e19452bd02c16b94630023c849aa490566816ab4d159b074c6a7fbf4"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.10493",
    "kind": "arxiv",
    "version": 1
  }
}