Pith Number

pith:HIK4DVRF

pith:2012:HIK4DVRFPXSOX54WME7BRRFXQG

not attested not anchored not stored refs pending

The curve complex has dead ends

Joan S. Birman, William W. Menasco

arxiv:1210.6698 v3 · 2012-10-24 · math.GT · math.GR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{HIK4DVRFPXSOX54WME7BRRFXQG}

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	2026-05-18T02:54:30.903020Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3a15c1d6257de4ebf796613e18c4b781a10b97c0f6ef18e06b5ff1ea2507ab3d

Aliases

arxiv: 1210.6698 · arxiv_version: 1210.6698v3 · doi: 10.48550/arxiv.1210.6698 · pith_short_12: HIK4DVRFPXSO · pith_short_16: HIK4DVRFPXSOX54W · pith_short_8: HIK4DVRF

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/HIK4DVRFPXSOX54WME7BRRFXQG \
  | 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: 3a15c1d6257de4ebf796613e18c4b781a10b97c0f6ef18e06b5ff1ea2507ab3d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "bca7d97755561611984401be814dd370c6ffa465dea22116fe069cf4f4a50bd5",
    "cross_cats_sorted": [
      "math.GR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2012-10-24T22:46:27Z",
    "title_canon_sha256": "38269e8724d567091f15fac2d19eedb0da88381f49069288a6149195dd62c95e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1210.6698",
    "kind": "arxiv",
    "version": 3
  }
}