Pith Number

pith:ND5MNKR7

pith:2024:ND5MNKR7GJAY4IXYOTZSRM75MG

not attested not anchored not stored refs pending

A Data-Driven Framework for Discovering Fractional Differential Equations in Complex Systems

Dongxiao Zhang, Hao Xu, HongGuang Sun, Xiangnan Yu, Yong Zhang, Yuntian Chen, Zhiping Mao

arxiv:2412.03970 v2 · 2024-12-05 · physics.comp-ph · cs.AI

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{ND5MNKR7GJAY4IXYOTZSRM75MG}

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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	2026-07-05T11:11:37.756193Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

68fac6aa3f32418e22f874f328b3fd61a17e292e31f17576cf79299d39405bba

Aliases

arxiv: 2412.03970 · arxiv_version: 2412.03970v2 · doi: 10.48550/arxiv.2412.03970 · pith_short_12: ND5MNKR7GJAY · pith_short_16: ND5MNKR7GJAY4IXY · pith_short_8: ND5MNKR7

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/ND5MNKR7GJAY4IXYOTZSRM75MG \
  | 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: 68fac6aa3f32418e22f874f328b3fd61a17e292e31f17576cf79299d39405bba

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f8247109b7f471ca96d8eb82ce294ec42e3c4b2fd4f1e25c71a1246c7d2a0a0e",
    "cross_cats_sorted": [
      "cs.AI"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "physics.comp-ph",
    "submitted_at": "2024-12-05T08:38:30Z",
    "title_canon_sha256": "1952f29e3c70fc86da6287aa44ed737f524f6daceb19fca18500449169a17f43"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2412.03970",
    "kind": "arxiv",
    "version": 2
  }
}