Pith Number

pith:Q34NONA3

pith:2011:Q34NONA3I6QEFZX7L2COUYW7XT

not attested not anchored not stored refs pending

Orbit Spaces of Gradient Vector Fields

Jack S. Calcut, Robert E. Gompf

arxiv:1105.5286 v2 · 2011-05-26 · math.DS · math.AT · math.GN

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{Q34NONA3I6QEFZX7L2COUYW7XT}

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	2026-05-18T02:45:49.893886Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

86f8d7341b47a042e6ff5e84ea62dfbcf569ac2e838683800ac68e9142286c7c

Aliases

arxiv: 1105.5286 · arxiv_version: 1105.5286v2 · doi: 10.48550/arxiv.1105.5286 · pith_short_12: Q34NONA3I6QE · pith_short_16: Q34NONA3I6QEFZX7 · pith_short_8: Q34NONA3

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/Q34NONA3I6QEFZX7L2COUYW7XT \
  | 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: 86f8d7341b47a042e6ff5e84ea62dfbcf569ac2e838683800ac68e9142286c7c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5a7d248ca68840277aa3d79664c1728f059b297a62f478254fe3ffcb2f0b37c9",
    "cross_cats_sorted": [
      "math.AT",
      "math.GN"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2011-05-26T13:42:20Z",
    "title_canon_sha256": "2eaac0c7127936f7568e17c585ce145d8096ed574678a866cfcabe46fc176ccd"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1105.5286",
    "kind": "arxiv",
    "version": 2
  }
}