Pith Number

pith:VS4GNCTP

pith:2007:VS4GNCTPVPEFCJQTKBEAVDDY27

not attested not anchored not stored refs pending

Colliding with a Crunching Bubble

Ben Freivogel, Gary T. Horowitz, Stephen Shenker

arxiv:hep-th/0703146 v1 · 2007-03-15 · hep-th · 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{VS4GNCTPVPEFCJQTKBEAVDDY27}

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

1 paper in Pith

Morse-Bott inequalities, Topology Change and Cobordisms to Nothing

Receipt and verification

First computed	2026-05-18T04:38:37.803980Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

acb8668a6fabc851261350480a8c78d7da169653c6d8cd94104a25de8bb44b89

Aliases

arxiv: hep-th/0703146 · arxiv_version: hep-th/0703146v1 · doi: 10.48550/arxiv.hep-th/0703146 · pith_short_12: VS4GNCTPVPEF · pith_short_16: VS4GNCTPVPEFCJQT · pith_short_8: VS4GNCTP

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/VS4GNCTPVPEFCJQTKBEAVDDY27 \
  | 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: acb8668a6fabc851261350480a8c78d7da169653c6d8cd94104a25de8bb44b89

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9c7a06c18852b3ec727ab975bfba33199cf1fe94264b3c93acd2a953557d79cf",
    "cross_cats_sorted": [
      "gr-qc"
    ],
    "license": "",
    "primary_cat": "hep-th",
    "submitted_at": "2007-03-15T18:56:39Z",
    "title_canon_sha256": "92ba0f80fb236d8b0ab82852ab97e2a23de255926082402e5fa62b263e6ff50e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "hep-th/0703146",
    "kind": "arxiv",
    "version": 1
  }
}