Pith Number

pith:I7T3HZB5

pith:2003:I7T3HZB5TI4O33JOTIV5A7NZCV

not attested not anchored not stored refs pending

A proof of Price's law for the collapse of a self-gravitating scalar field

Igor Rodnianski, Mihalis Dafermos

arxiv:gr-qc/0309115 v3 · 2003-09-23 · gr-qc · math.AP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{I7T3HZB5TI4O33JOTIV5A7NZCV}

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	2026-05-18T01:39:22.880861Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

47e7b3e43d9a38eded2e9a2bd07db91576479e9cb5970f29cfafee9f9b5ea408

Aliases

arxiv: gr-qc/0309115 · arxiv_version: gr-qc/0309115v3 · doi: 10.48550/arxiv.gr-qc/0309115 · pith_short_12: I7T3HZB5TI4O · pith_short_16: I7T3HZB5TI4O33JO · pith_short_8: I7T3HZB5

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/I7T3HZB5TI4O33JOTIV5A7NZCV \
  | 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: 47e7b3e43d9a38eded2e9a2bd07db91576479e9cb5970f29cfafee9f9b5ea408

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ab0e1c05a19ce8e4bbce52aa6ccd838ee797efacc2c713a42e09b37e93c4998e",
    "cross_cats_sorted": [
      "math.AP"
    ],
    "license": "",
    "primary_cat": "gr-qc",
    "submitted_at": "2003-09-23T20:06:02Z",
    "title_canon_sha256": "3277306713a3c68fd75d1e71c14f5331f533a961f8c13b43ac944d66e6c4d8c3"
  },
  "schema_version": "1.0",
  "source": {
    "id": "gr-qc/0309115",
    "kind": "arxiv",
    "version": 3
  }
}