Pith Number

pith:R3ECSA6C

pith:2014:R3ECSA6C357PNB3OAPEN6DTAK5

not attested not anchored not stored refs pending

Smooth functions on 2-torus whose Kronrod-Reeb graph contains a cycle

Bohdan Feshchenko, Sergiy Maksymenko

arxiv:1411.6863 v1 · 2014-11-25 · 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{R3ECSA6C357PNB3OAPEN6DTAK5}

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	2026-05-18T02:32:47.132049Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

8ec82903c2df7ef6876e03c8df0e60576b455c42145022c23c5833f711a513a6

Aliases

arxiv: 1411.6863 · arxiv_version: 1411.6863v1 · doi: 10.48550/arxiv.1411.6863 · pith_short_12: R3ECSA6C357P · pith_short_16: R3ECSA6C357PNB3O · pith_short_8: R3ECSA6C

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/R3ECSA6C357PNB3OAPEN6DTAK5 \
  | 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: 8ec82903c2df7ef6876e03c8df0e60576b455c42145022c23c5833f711a513a6

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8546a6ac783e9b079512befcf7a304024da82467d2381c5b4b0bf00ce96f5e65",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2014-11-25T13:37:16Z",
    "title_canon_sha256": "d78780489a23de29b9a4c2c9b118fd5fea1edb7ca6ab9719f5df0d888ee9c2a2"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1411.6863",
    "kind": "arxiv",
    "version": 1
  }
}