Pith Number

pith:HJTMIA7F

pith:2025:HJTMIA7FAJFSRFGIBSTL2N3KZ3

not attested not anchored not stored refs pending

Recursive Hierarchical Networks and the Law of Functional Evolution: A Universal Framework for Complex Systems

Hui Li, Yanxin Li

arxiv:2509.05567 v2 · 2025-09-06 · physics.soc-ph · cs.SI · nlin.AO · physics.data-an

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{HJTMIA7FAJFSRFGIBSTL2N3KZ3}

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	2026-05-20T01:04:56.972393Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3a66c403e5024b2894c80ca6bd376acedb1bdf0b6f28277ce46adafebc85150a

Aliases

arxiv: 2509.05567 · arxiv_version: 2509.05567v2 · doi: 10.48550/arxiv.2509.05567 · pith_short_12: HJTMIA7FAJFS · pith_short_16: HJTMIA7FAJFSRFGI · pith_short_8: HJTMIA7F

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/HJTMIA7FAJFSRFGIBSTL2N3KZ3 \
  | 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: 3a66c403e5024b2894c80ca6bd376acedb1bdf0b6f28277ce46adafebc85150a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "43f56b4da076fbfefab948bbceeecc8be3c44e814d5f755a69f7692a914fb34a",
    "cross_cats_sorted": [
      "cs.SI",
      "nlin.AO",
      "physics.data-an"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "physics.soc-ph",
    "submitted_at": "2025-09-06T02:49:21Z",
    "title_canon_sha256": "bf5536ec3e8579a0496705c7fd63d67c3c6dcbabc5f776b72ce873c1b3ec9217"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2509.05567",
    "kind": "arxiv",
    "version": 2
  }
}