Pith Number

pith:MMKKZZVP

pith:2013:MMKKZZVPHZUFTTATKBOMWFLO7Y

not attested not anchored not stored refs pending

Composite tunnel number one genus two handlebody-knots

Makoto Ozawa, Mario Eudave-Munoz

arxiv:1305.3410 v1 · 2013-05-15 · 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{MMKKZZVPHZUFTTATKBOMWFLO7Y}

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	2026-05-18T03:25:35.870140Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6314ace6af3e6859cc13505ccb156efe02cbd650f9f7eda46c47dce1d41106c5

Aliases

arxiv: 1305.3410 · arxiv_version: 1305.3410v1 · doi: 10.48550/arxiv.1305.3410 · pith_short_12: MMKKZZVPHZUF · pith_short_16: MMKKZZVPHZUFTTAT · pith_short_8: MMKKZZVP

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/MMKKZZVPHZUFTTATKBOMWFLO7Y \
  | 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: 6314ace6af3e6859cc13505ccb156efe02cbd650f9f7eda46c47dce1d41106c5

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "70f375cbb85195451a85125b0088514aa74207c577382b973929f161de5b6c88",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2013-05-15T10:05:07Z",
    "title_canon_sha256": "1487cd3f3cfcd87e578e78cacdbaff79a752f7dba618d5f9fb9af597691b354c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1305.3410",
    "kind": "arxiv",
    "version": 1
  }
}