Pith Number

pith:QS5N5Z5L

pith:2009:QS5N5Z5L76IQWGX5R2GUOXKDYU

not attested not anchored not stored refs pending

Phase Transitions in Gravitational Allocation

Dan Romik, Ron Peled, Sourav Chatterjee, Yuval Peres

arxiv:0903.4647 v1 · 2009-03-26 · math.PR · 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{QS5N5Z5L76IQWGX5R2GUOXKDYU}

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	2026-05-18T00:48:55.645591Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

84badee7abff910b1afd8e8d475d43c53cc1c1b004784d64cdbf358a3e8d8dc9

Aliases

arxiv: 0903.4647 · arxiv_version: 0903.4647v1 · doi: 10.48550/arxiv.0903.4647 · pith_short_12: QS5N5Z5L76IQ · pith_short_16: QS5N5Z5L76IQWGX5 · pith_short_8: QS5N5Z5L

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/QS5N5Z5L76IQWGX5R2GUOXKDYU \
  | 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: 84badee7abff910b1afd8e8d475d43c53cc1c1b004784d64cdbf358a3e8d8dc9

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "dd2f9ac5b19cbbce038f34110c6cbd11ca0fdfa2b96ead42a15c7a42e4e1640a",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2009-03-26T17:36:19Z",
    "title_canon_sha256": "c64b9c1ee10604f54fe9dc21eb37bc395339469ceab1b1b6d354cf3a19abad0f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0903.4647",
    "kind": "arxiv",
    "version": 1
  }
}