Pith Number

pith:ZBB42K55

pith:1994:ZBB42K55HTE2L3VQW427KVICV7

not attested not anchored not stored refs pending

Global structure of Witten's 2+1 gravity on ${\bf R}\times T^2$

Donald Marolf, Jorma Louko

arxiv:gr-qc/9403041 v1 · 1994-03-21 · gr-qc · hep-th

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{ZBB42K55HTE2L3VQW427KVICV7}

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	2026-07-04T14:26:00.422502Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c843cd2bbd3cc9a5eeb0b735f55502afde2e52bd9a40e297ccc3c50f9b42a854

Aliases

arxiv: gr-qc/9403041 · arxiv_version: gr-qc/9403041v1 · doi: 10.48550/arxiv.gr-qc/9403041 · pith_short_12: ZBB42K55HTE2 · pith_short_16: ZBB42K55HTE2L3VQ · pith_short_8: ZBB42K55

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/ZBB42K55HTE2L3VQW427KVICV7 \
  | 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: c843cd2bbd3cc9a5eeb0b735f55502afde2e52bd9a40e297ccc3c50f9b42a854

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ecac822bb57d9dd8e928f20c150183781c6e1f40944bcab45167dc66534719da",
    "cross_cats_sorted": [
      "hep-th"
    ],
    "license": "",
    "primary_cat": "gr-qc",
    "submitted_at": "1994-03-21T15:39:52Z",
    "title_canon_sha256": "6fd89afa4c54f21e641a1804dc3d5d555ef8f37927f145e7ab41d4c69db17ec8"
  },
  "schema_version": "1.0",
  "source": {
    "id": "gr-qc/9403041",
    "kind": "arxiv",
    "version": 1
  }
}