Pith Number

pith:TPPACGMH

pith:2011:TPPACGMHASDOZ2KZQKSD4642K4

not attested not anchored not stored refs pending

Macroscopic limits and phase transition in a system of self-propelled particles

Amic Frouvelle (IMT), Jian-Guo Liu, Pierre Degond (IMT)

arxiv:1109.2404 v1 · 2011-09-12 · 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{TPPACGMHASDOZ2KZQKSD4642K4}

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	2026-05-18T02:42:06.394254Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9bde0119870486ece95982a43e7b9a57139ae332b3c34d72d31517391b64262b

Aliases

arxiv: 1109.2404 · arxiv_version: 1109.2404v1 · doi: 10.48550/arxiv.1109.2404 · pith_short_12: TPPACGMHASDO · pith_short_16: TPPACGMHASDOZ2KZ · pith_short_8: TPPACGMH

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/TPPACGMHASDOZ2KZQKSD4642K4 \
  | 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: 9bde0119870486ece95982a43e7b9a57139ae332b3c34d72d31517391b64262b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8a649bb5b7584be53799e736912c5c79cb3e702ce4cacac5e3756edd3a5042c9",
    "cross_cats_sorted": [
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2011-09-12T08:40:08Z",
    "title_canon_sha256": "0237b2ab8fd221932540989fbb3e3e5ee706018319f1afaa7994b42c1663822e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1109.2404",
    "kind": "arxiv",
    "version": 1
  }
}