Pith Number

pith:T47WWFUE

pith:2012:T47WWFUEYCWU3VCMGCKB4G3TYZ

not attested not anchored not stored refs pending

On non-smooth vector fields having a torus or a sphere as the sliding manifold

Ricardo Miranda Martins

arxiv:1207.0397 v1 · 2012-07-02 · math.DS

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{T47WWFUEYCWU3VCMGCKB4G3TYZ}

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	2026-05-18T03:51:59.428519Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9f3f6b1684c0ad4dd44c30941e1b73c661afc074d69755b96c0242baac04380b

Aliases

arxiv: 1207.0397 · arxiv_version: 1207.0397v1 · doi: 10.48550/arxiv.1207.0397 · pith_short_12: T47WWFUEYCWU · pith_short_16: T47WWFUEYCWU3VCM · pith_short_8: T47WWFUE

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/T47WWFUEYCWU3VCMGCKB4G3TYZ \
  | 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: 9f3f6b1684c0ad4dd44c30941e1b73c661afc074d69755b96c0242baac04380b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1c6bf4425f421c6da27a442cdb8cf8f6285db1d1575e46fc5db92e79564cb3c0",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2012-07-02T14:19:22Z",
    "title_canon_sha256": "60b28be6e1bdad975b9d5994fde2fb3f3827a8d265bbc42ec46c3d32c2a2e601"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1207.0397",
    "kind": "arxiv",
    "version": 1
  }
}