Pith Number

pith:W5PPHMJ3

pith:2012:W5PPHMJ3Q6LKIBFUOCDYBWYHAD

not attested not anchored not stored refs pending

Common zeros of inward vector fields on surfaces

Morris W. Hirsch

arxiv:1204.1301 v3 · 2012-04-05 · math.DS · math.GR · 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{W5PPHMJ3Q6LKIBFUOCDYBWYHAD}

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	2026-05-18T03:56:47.346466Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b75ef3b13b8796a404b4708780db0700d369339d0cedd9910a8bb3954daa024f

Aliases

arxiv: 1204.1301 · arxiv_version: 1204.1301v3 · doi: 10.48550/arxiv.1204.1301 · pith_short_12: W5PPHMJ3Q6LK · pith_short_16: W5PPHMJ3Q6LKIBFU · pith_short_8: W5PPHMJ3

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/W5PPHMJ3Q6LKIBFUOCDYBWYHAD \
  | 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: b75ef3b13b8796a404b4708780db0700d369339d0cedd9910a8bb3954daa024f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6b486d9105cc903e0b51bea92384d3f18477357bab6de30dffcd1c6430bb7319",
    "cross_cats_sorted": [
      "math.GR",
      "math.GT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2012-04-05T18:32:10Z",
    "title_canon_sha256": "d30085923806cff1150d6a333e2c08fc44868a248c34d503dded30ea1c88266b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1204.1301",
    "kind": "arxiv",
    "version": 3
  }
}