Pith Number

pith:AYB6GXOD

pith:1998:AYB6GXODBX66QSKGOQADL4OWLF

not attested not anchored not stored refs pending

Virtual homology of surgered torus bundles

Joseph D. Masters

arxiv:math/9812068 v1 · 1998-12-11 · 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{AYB6GXODBX66QSKGOQADL4OWLF}

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	2026-05-18T01:05:33.461890Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0603e35dc30dfde84946740035f1d659465c1e1647620f2be3eda0cc1dc78a32

Aliases

arxiv: math/9812068 · arxiv_version: math/9812068v1 · doi: 10.48550/arxiv.math/9812068 · pith_short_12: AYB6GXODBX66 · pith_short_16: AYB6GXODBX66QSKG · pith_short_8: AYB6GXOD

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/AYB6GXODBX66QSKGOQADL4OWLF \
  | 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: 0603e35dc30dfde84946740035f1d659465c1e1647620f2be3eda0cc1dc78a32

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ba699ddf67e43a17681f10d3e997e02e56a640b82a36b200c3137315f9e2d820",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "math.GT",
    "submitted_at": "1998-12-11T05:04:52Z",
    "title_canon_sha256": "6e185b8c647e927de8a66a8eb6bf0311e5afbb0e247abb2b122f6b31b4860d22"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/9812068",
    "kind": "arxiv",
    "version": 1
  }
}