Pith Number

pith:NSH2XA7O

pith:2012:NSH2XA7OECGFDODS4BQGTPXUD2

not attested not anchored not stored refs pending

Minoration of the complexity function associated to a translation on the torus

Jean Fran\c{c}ois Bertazzon, Nicolas B\'edaride

arxiv:1207.2984 v4 · 2012-07-12 · math.DS · math.CO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{NSH2XA7OECGFDODS4BQGTPXUD2}

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	2026-05-18T01:10:55.027665Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6c8fab83ee208c51b872e06069bef41eafb887ddfbaa1a08de3cff44bde309ae

Aliases

arxiv: 1207.2984 · arxiv_version: 1207.2984v4 · doi: 10.48550/arxiv.1207.2984 · pith_short_12: NSH2XA7OECGF · pith_short_16: NSH2XA7OECGFDODS · pith_short_8: NSH2XA7O

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/NSH2XA7OECGFDODS4BQGTPXUD2 \
  | 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: 6c8fab83ee208c51b872e06069bef41eafb887ddfbaa1a08de3cff44bde309ae

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "729b89c0371bd94ea7c67bebcf162ebd10087e29a116b90278d37820c6e63f49",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2012-07-12T14:33:01Z",
    "title_canon_sha256": "007c2f2d7aa8d5abf3a6eb64291c8d3a7bef1fc803d200e748bf3cbffe370989"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1207.2984",
    "kind": "arxiv",
    "version": 4
  }
}