Pith Number

pith:22GPOTM4

pith:2016:22GPOTM4AP4ZDMDPOPFIBSWGWL

not attested not anchored not stored refs pending

Genera and minors of multibranched surfaces

Makoto Ozawa, Shosaku Matsuzaki

arxiv:1603.09041 v1 · 2016-03-30 · math.GT · math.AT · math.CO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{22GPOTM4AP4ZDMDPOPFIBSWGWL}

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	2026-05-18T01:18:03.910675Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d68cf74d9c03f991b06f73ca80cac6b2ecfb2bb5b050ef37112ad3c292921dba

Aliases

arxiv: 1603.09041 · arxiv_version: 1603.09041v1 · doi: 10.48550/arxiv.1603.09041 · pith_short_12: 22GPOTM4AP4Z · pith_short_16: 22GPOTM4AP4ZDMDP · pith_short_8: 22GPOTM4

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/22GPOTM4AP4ZDMDPOPFIBSWGWL \
  | 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: d68cf74d9c03f991b06f73ca80cac6b2ecfb2bb5b050ef37112ad3c292921dba

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e912eae19ddd3ef3ce760e0bca4003b95bb9e97003f971f1578e370ab88efcb8",
    "cross_cats_sorted": [
      "math.AT",
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2016-03-30T05:16:17Z",
    "title_canon_sha256": "bcaf7479f43a0cc808161a254323f524abb7e497ffae68d8939c44822ff36ec0"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1603.09041",
    "kind": "arxiv",
    "version": 1
  }
}