Pith Number

pith:XWH2WXT7

pith:2015:XWH2WXT7YE2N7DALQQ2LCYVKIF

not attested not anchored not stored refs pending

Boundary-reducing surgeries and bridge number

John Luecke, Kenneth L. Baker, R. Sean Bowman

arxiv:1512.09336 v1 · 2015-12-31 · 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{XWH2WXT7YE2N7DALQQ2LCYVKIF}

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	2026-05-18T01:23:32.654968Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

bd8fab5e7fc134df8c0b8434b162aa417454e28f20267a0cdf23851e1f776b37

Aliases

arxiv: 1512.09336 · arxiv_version: 1512.09336v1 · doi: 10.48550/arxiv.1512.09336 · pith_short_12: XWH2WXT7YE2N · pith_short_16: XWH2WXT7YE2N7DAL · pith_short_8: XWH2WXT7

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/XWH2WXT7YE2N7DALQQ2LCYVKIF \
  | 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: bd8fab5e7fc134df8c0b8434b162aa417454e28f20267a0cdf23851e1f776b37

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "329fd904a613d3c0b8e0ea420f5e5aef2e1dc429a87e6346f953e375f4bb4085",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2015-12-31T18:37:37Z",
    "title_canon_sha256": "25532bc68c18ae80c04f966362755dd5401e5921957469d641e55f73bbed73b9"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1512.09336",
    "kind": "arxiv",
    "version": 1
  }
}