Pith Number

pith:W6VV5MMA

pith:1998:W6VV5MMAU6ISUGGNHPXXNPYGDT

not attested not anchored not stored refs pending

Kirby calculus in manifolds with boundary

Justin Roberts

arxiv:math/9812086 v1 · 1998-12-15 · 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{W6VV5MMAU6ISUGGNHPXXNPYGDT}

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	2026-07-04T14:40:54.303581Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b7ab5eb180a7912a18cd3bef76bf061cf879a41824d1359e3b911f618618dfdb

Aliases

arxiv: math/9812086 · arxiv_version: math/9812086v1 · doi: 10.48550/arxiv.math/9812086 · pith_short_12: W6VV5MMAU6IS · pith_short_16: W6VV5MMAU6ISUGGN · pith_short_8: W6VV5MMA

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/W6VV5MMAU6ISUGGNHPXXNPYGDT \
  | 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: b7ab5eb180a7912a18cd3bef76bf061cf879a41824d1359e3b911f618618dfdb

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ddfdd63c6465deecbf72c311c14c765220684ff73da5d849ed4e9570992e9484",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "math.GT",
    "submitted_at": "1998-12-15T17:27:41Z",
    "title_canon_sha256": "1878b39c54883d6e6e21ffc47ce2545a3ce5e7dc95e40fb45508fd055fe7a649"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/9812086",
    "kind": "arxiv",
    "version": 1
  }
}