Pith Number

pith:BBEC7LWT

pith:2025:BBEC7LWT7O6Z6ANEOUFUUY4Q66

not attested not anchored not stored refs pending

Semi-Global Existence and Trapped Surface Formation for the Einstein-Vlasov System

Nikolaos Athanasiou, Puskar Mondal, Shing-Tung Yau

arxiv:2510.12429 v2 · 2025-10-14 · math.AP · gr-qc · math-ph · math.DG · 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{BBEC7LWT7O6Z6ANEOUFUUY4Q66}

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	2026-07-07T01:15:59.359132Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

08482faed3fbbd9f01a4750b4a6390f79ece57ab5b7e520787443514fabd5f39

Aliases

arxiv: 2510.12429 · arxiv_version: 2510.12429v2 · doi: 10.48550/arxiv.2510.12429 · pith_short_12: BBEC7LWT7O6Z · pith_short_16: BBEC7LWT7O6Z6ANE · pith_short_8: BBEC7LWT

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/BBEC7LWT7O6Z6ANEOUFUUY4Q66 \
  | 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: 08482faed3fbbd9f01a4750b4a6390f79ece57ab5b7e520787443514fabd5f39

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4664e1d878728ecef15aa6d667ac300867d9477276186e0f4508f4766f06ca62",
    "cross_cats_sorted": [
      "gr-qc",
      "math-ph",
      "math.DG",
      "math.MP"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2025-10-14T12:07:19Z",
    "title_canon_sha256": "72126b8b63f536cb484fbf1aa8f5ad000f04a88280c152362c1abfa2e4d24481"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2510.12429",
    "kind": "arxiv",
    "version": 2
  }
}