Pith Number

pith:6BB5EE6T

pith:2010:6BB5EE6T64TXY2PAEMWWC2RX5O

not attested not anchored not stored refs pending

Singularity theorems based on trapped submanifolds of arbitrary co-dimension

Gregory J. Galloway, Jos\'e M. M. Senovilla

arxiv:1005.1249 v2 · 2010-05-07 · 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{6BB5EE6T64TXY2PAEMWWC2RX5O}

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.

Cited by

2 papers in Pith

Curvature conditions for generalized singularity theorems

Convex foliations and trapped submanifolds

Receipt and verification

First computed	2026-05-18T02:33:32.492013Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f043d213d3f7277c69e0232d616a37eb9283ac45cfc56fe66e4a8c92d0de6ec5

Aliases

arxiv: 1005.1249 · arxiv_version: 1005.1249v2 · doi: 10.48550/arxiv.1005.1249 · pith_short_12: 6BB5EE6T64TX · pith_short_16: 6BB5EE6T64TXY2PA · pith_short_8: 6BB5EE6T

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/6BB5EE6T64TXY2PAEMWWC2RX5O \
  | 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: f043d213d3f7277c69e0232d616a37eb9283ac45cfc56fe66e4a8c92d0de6ec5

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "024105ce2c5ee0fadb1c0cc429919defe76064538e57acfa78ae9ba5156422c4",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "gr-qc",
    "submitted_at": "2010-05-07T16:52:03Z",
    "title_canon_sha256": "40a7ec382940c55e06fab0d64d7cf9816873930544ed57409d5700fe3f83a5f4"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1005.1249",
    "kind": "arxiv",
    "version": 2
  }
}