Pith Number

pith:6YJWR2QX

pith:2000:6YJWR2QX2QOKJ7S7JIATKV2FWG

not attested not anchored not stored refs pending

On the geometric boundaries of hyperbolic 4-manifolds

A. W. Reid, Darren D. Long

arxiv:math/0007197 v1 · 2000-07-19 · math.GT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{6YJWR2QX2QOKJ7S7JIATKV2FWG}

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	2026-05-18T02:38:00.969538Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f61368ea17d41ca4fe5f4a01355745b1a2d058aa4115664b12b13a705ba8626a

Aliases

arxiv: math/0007197 · arxiv_version: math/0007197v1 · doi: 10.48550/arxiv.math/0007197 · pith_short_12: 6YJWR2QX2QOK · pith_short_16: 6YJWR2QX2QOKJ7S7 · pith_short_8: 6YJWR2QX

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/6YJWR2QX2QOKJ7S7JIATKV2FWG \
  | 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: f61368ea17d41ca4fe5f4a01355745b1a2d058aa4115664b12b13a705ba8626a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "bc91c08f766e45b988530cc8273f83dade0497073f1c3c15689b539e4c9940cc",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "math.GT",
    "submitted_at": "2000-07-19T00:00:00Z",
    "title_canon_sha256": "dbcfbd7b1b960975e576884a5e434702357a70db2ab930b62e8279eb95b7f433"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0007197",
    "kind": "arxiv",
    "version": 1
  }
}