Pith Number

pith:WIBYZMUA

pith:2026:WIBYZMUAISCPU2LGN5AR6RWF6W

not attested not anchored not stored refs pending

Evolution of Hawking mass under perturbative spacetime uniformly expanding flows

Hollis Williams

arxiv:2601.12013 v2 · 2026-01-17 · gr-qc

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{WIBYZMUAISCPU2LGN5AR6RWF6W}

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	2026-05-26T01:03:22.636542Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b2038cb2804484fa69666f411f46c5f585617c06e430c890a3b09e907841baa8

Aliases

arxiv: 2601.12013 · arxiv_version: 2601.12013v2 · doi: 10.48550/arxiv.2601.12013 · pith_short_12: WIBYZMUAISCP · pith_short_16: WIBYZMUAISCPU2LG · pith_short_8: WIBYZMUA

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/WIBYZMUAISCPU2LGN5AR6RWF6W \
  | 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: b2038cb2804484fa69666f411f46c5f585617c06e430c890a3b09e907841baa8

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c2acc58b5a1a6169ceb46350ee7201984185e2245b23dfbbfc8fbac223ad47f3",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "gr-qc",
    "submitted_at": "2026-01-17T11:39:35Z",
    "title_canon_sha256": "3c0cfa7298fd23de6f2fff9609887516e93158e436312bafb425ece0568f1792"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2601.12013",
    "kind": "arxiv",
    "version": 2
  }
}