Pith Number

pith:ZFLF6S4S

pith:2012:ZFLF6S4S7KGD3PMU66O5TGRFWU

not attested not anchored not stored refs pending

There is no triangulation of the torus with vertex degrees 5, 6, ..., 6, 7 and related results: Geometric proofs for combinatorial theorems

Boris Springborn, G\"unter Rote, Ivan Izmestiev, John M. Sullivan, Robert B. Kusner

arxiv:1207.3605 v2 · 2012-07-16 · math.CO · 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{ZFLF6S4S7KGD3PMU66O5TGRFWU}

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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	2026-05-18T03:13:21.897789Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c9565f4b92fa8c3dbd94f79dd99a25b50c7fa89a40dc6f48ca00dff2c314eec1

Aliases

arxiv: 1207.3605 · arxiv_version: 1207.3605v2 · doi: 10.48550/arxiv.1207.3605 · pith_short_12: ZFLF6S4S7KGD · pith_short_16: ZFLF6S4S7KGD3PMU · pith_short_8: ZFLF6S4S

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/ZFLF6S4S7KGD3PMU66O5TGRFWU \
  | 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: c9565f4b92fa8c3dbd94f79dd99a25b50c7fa89a40dc6f48ca00dff2c314eec1

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a951088b9b14024ecc1ecfe50fef137cb45333227cbe180978c498a5743bac82",
    "cross_cats_sorted": [
      "math.GT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2012-07-16T09:02:29Z",
    "title_canon_sha256": "0e1b0807a915d8fbe0cad8eebd3e49c706fb6ab4073fd44c4c7fd584118f7837"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1207.3605",
    "kind": "arxiv",
    "version": 2
  }
}