Pith Number

pith:ZOEVM6JM

pith:2012:ZOEVM6JMP4EDTSY6FWBSLGWZ6P

not attested not anchored not stored refs pending

A mean field model for the collective behaviour of interacting multi-species particles. Mathematical results and application to the inverse problem

M. Fedele

arxiv:1212.3649 v1 · 2012-12-15 · math-ph · 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{ZOEVM6JMP4EDTSY6FWBSLGWZ6P}

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	2026-05-18T03:38:22.763327Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

cb8956792c7f0839cb1e2d83259ad9f3e76238961f19e44b665e8bb193ada489

Aliases

arxiv: 1212.3649 · arxiv_version: 1212.3649v1 · doi: 10.48550/arxiv.1212.3649 · pith_short_12: ZOEVM6JMP4ED · pith_short_16: ZOEVM6JMP4EDTSY6 · pith_short_8: ZOEVM6JM

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/ZOEVM6JMP4EDTSY6FWBSLGWZ6P \
  | 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: cb8956792c7f0839cb1e2d83259ad9f3e76238961f19e44b665e8bb193ada489

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5e986a26140f5d2189a53d3cf642f5151819572b4df82426ecb7df8c7e0e8b4c",
    "cross_cats_sorted": [
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2012-12-15T01:43:39Z",
    "title_canon_sha256": "53c2120ec5e361783bb0ad70319ca7cc31c32b83f9435a96b1aecd0e5fabf553"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1212.3649",
    "kind": "arxiv",
    "version": 1
  }
}