Pith Number

pith:3MTYQQSN

pith:2013:3MTYQQSNXV2WXWEIG3GVYL3QAJ

not attested not anchored not stored refs pending

Multiplicative decomposition of arithmetic progressions in prime fields

M. Z. Garaev, S. V. Konyagin

arxiv:1309.6980 v1 · 2013-09-26 · 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{3MTYQQSNXV2WXWEIG3GVYL3QAJ}

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	2026-05-18T03:12:09.586805Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

db2788424dbd756bd88836cd5c2f70025d724c3705844beb2f65d09c34be74f8

Aliases

arxiv: 1309.6980 · arxiv_version: 1309.6980v1 · doi: 10.48550/arxiv.1309.6980 · pith_short_12: 3MTYQQSNXV2W · pith_short_16: 3MTYQQSNXV2WXWEI · pith_short_8: 3MTYQQSN

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/3MTYQQSNXV2WXWEIG3GVYL3QAJ \
  | 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: db2788424dbd756bd88836cd5c2f70025d724c3705844beb2f65d09c34be74f8

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "48f448fd96e670ba470504e3ba363ff685289284e86045b059eb51000d9c8ed2",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2013-09-26T17:19:12Z",
    "title_canon_sha256": "1db0f1d116259bf86dbad03f4ab585a21e6cf2b22ca184d186d5cab9084a6c2a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1309.6980",
    "kind": "arxiv",
    "version": 1
  }
}