Pith Number

pith:VMKCYTTP

pith:2017:VMKCYTTPXUIQNRC5K4UPJDVEVU

not attested not anchored not stored refs pending

Simplifying branched covering surface-knots by chart moves involving black vertices

Inasa Nakamura

arxiv:1709.07762 v2 · 2017-09-21 · 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{VMKCYTTPXUIQNRC5K4UPJDVEVU}

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	2026-05-18T00:05:19.665805Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ab142c4e6fbd1106c45d5728f48ea4ad3827c222b7b21970dd4c00965222538a

Aliases

arxiv: 1709.07762 · arxiv_version: 1709.07762v2 · doi: 10.48550/arxiv.1709.07762 · pith_short_12: VMKCYTTPXUIQ · pith_short_16: VMKCYTTPXUIQNRC5 · pith_short_8: VMKCYTTP

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/VMKCYTTPXUIQNRC5K4UPJDVEVU \
  | 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: ab142c4e6fbd1106c45d5728f48ea4ad3827c222b7b21970dd4c00965222538a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "fe32d4c4a5947d6b28ddabf96250995c060d1b2321df6c96eeaa984e17cc1402",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2017-09-21T11:20:35Z",
    "title_canon_sha256": "579f12c7fe55e72d35ae7f65c95f7f04b926cb9bb5e2f2526cd86f66147d6120"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1709.07762",
    "kind": "arxiv",
    "version": 2
  }
}