Pith Number

pith:FGY7OAS2

pith:2024:FGY7OAS2KQ7Q2ZZMXRMKVTQY3A

not attested not anchored not stored refs pending

Formation of Trapped Surfaces in Geodesic Foliation

Sergiu Klainerman, Xuantao Chen

arxiv:2409.14582 v1 · 2024-09-22 · gr-qc · math.AP · math.DG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{FGY7OAS2KQ7Q2ZZMXRMKVTQY3A}

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	2026-07-05T09:10:18.839777Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

29b1f7025a543f0d672cbc58aace18d812f5806fda60d410cc00de7c01f80840

Aliases

arxiv: 2409.14582 · arxiv_version: 2409.14582v1 · doi: 10.48550/arxiv.2409.14582 · pith_short_12: FGY7OAS2KQ7Q · pith_short_16: FGY7OAS2KQ7Q2ZZM · pith_short_8: FGY7OAS2

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/FGY7OAS2KQ7Q2ZZMXRMKVTQY3A \
  | 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: 29b1f7025a543f0d672cbc58aace18d812f5806fda60d410cc00de7c01f80840

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "99d9090dd1f157d3b0775b0cf7c2456365caf5ca31535cb3daaad073e572ee75",
    "cross_cats_sorted": [
      "math.AP",
      "math.DG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "gr-qc",
    "submitted_at": "2024-09-22T20:01:09Z",
    "title_canon_sha256": "7105f93e9301df8edf69eeda19758ce16bc891e285f721644ab16911e083b38c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2409.14582",
    "kind": "arxiv",
    "version": 1
  }
}