Pith Number

pith:4FU6CFW2

pith:2011:4FU6CFW2MV27E7VT3Z3ZRHOJF6

not attested not anchored not stored refs pending

The behaviour of curvature functions at cusps and inflection points

Masaaki Umehara, Shohei Shiba

arxiv:1102.4478 v1 · 2011-02-22 · math.DG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{4FU6CFW2MV27E7VT3Z3ZRHOJF6}

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	2026-05-18T04:28:08.850699Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e169e116da6575f27eb3de77989dc92f81b075e796d155fec1d5ca7b1c09eaff

Aliases

arxiv: 1102.4478 · arxiv_version: 1102.4478v1 · doi: 10.48550/arxiv.1102.4478 · pith_short_12: 4FU6CFW2MV27 · pith_short_16: 4FU6CFW2MV27E7VT · pith_short_8: 4FU6CFW2

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/4FU6CFW2MV27E7VT3Z3ZRHOJF6 \
  | 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: e169e116da6575f27eb3de77989dc92f81b075e796d155fec1d5ca7b1c09eaff

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6f8d520b9add16f1769c58e8d59f669fed6a064c97ee01f8b5fca9e0b0d27906",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2011-02-22T12:11:05Z",
    "title_canon_sha256": "f01996df771f88db3a5a4062d347c0ed73e3f175a82bc60e2dcc678aacac1bbb"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1102.4478",
    "kind": "arxiv",
    "version": 1
  }
}