Pith Number

pith:NINMBZDL

pith:2012:NINMBZDLECJGW52JYDDK7QTSC2

not attested not anchored not stored refs pending

Periodic Sequences modulo $m$

Alexandre Laugier, Manjil Saikia

arxiv:1209.2371 v3 · 2012-09-10 · math.NT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{NINMBZDLECJGW52JYDDK7QTSC2}

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.

Cited by

1 paper in Pith

Optimal Lower Bounds for Symmetric Modular Circuits

Receipt and verification

First computed	2026-05-18T01:32:01.550247Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6a1ac0e46b20926b7749c0c6afc27216831c23ec7b0ba977f2ada64f604dde0d

Aliases

arxiv: 1209.2371 · arxiv_version: 1209.2371v3 · doi: 10.48550/arxiv.1209.2371 · pith_short_12: NINMBZDLECJG · pith_short_16: NINMBZDLECJGW52J · pith_short_8: NINMBZDL

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/NINMBZDLECJGW52JYDDK7QTSC2 \
  | 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: 6a1ac0e46b20926b7749c0c6afc27216831c23ec7b0ba977f2ada64f604dde0d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3336f338dfed752d8a3f689becdd0876f4296d6bc184d63d20bfb85b8720636e",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2012-09-10T15:46:43Z",
    "title_canon_sha256": "b0ea5e8dab64ea7dd08fa5a92ab1abc65f2ecc4a694e1382915b383595a7d760"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1209.2371",
    "kind": "arxiv",
    "version": 3
  }
}