Pith Number

pith:CN22JZZU

pith:2024:CN22JZZUYV76NV7CFLSP2OSFPW

not attested not anchored not stored refs pending

From microscopic to macroscopic: the large number dynamics of agents and cells, possibly interacting with a chemical background

Thierry Paul (LYSM)

arxiv:2406.06180 v1 · 2024-06-10 · math.AP · math.DS · physics.class-ph

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{CN22JZZUYV76NV7CFLSP2OSFPW}

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	2026-07-05T08:29:38.886253Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1375a4e734c57fe6d7e22ae4fd3a457d9494272642afc933dcfbbf2d41b63656

Aliases

arxiv: 2406.06180 · arxiv_version: 2406.06180v1 · doi: 10.48550/arxiv.2406.06180 · pith_short_12: CN22JZZUYV76 · pith_short_16: CN22JZZUYV76NV7C · pith_short_8: CN22JZZU

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/CN22JZZUYV76NV7CFLSP2OSFPW \
  | 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: 1375a4e734c57fe6d7e22ae4fd3a457d9494272642afc933dcfbbf2d41b63656

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "75da7fa19e3e00fcf7e2a8377ad31828d7be8ab7e276d83d5927095b5a356539",
    "cross_cats_sorted": [
      "math.DS",
      "physics.class-ph"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2024-06-10T11:25:09Z",
    "title_canon_sha256": "f4c26e9fac0ff28bb3008ecabc64a8f02c6763bf1c30e1c1383f9581f8bc7d82"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2406.06180",
    "kind": "arxiv",
    "version": 1
  }
}