Pith Number

pith:TAMNJ3IZ

pith:2015:TAMNJ3IZELKHY5BPD3AHRTK5VZ

not attested not anchored not stored refs pending

Geometric Progression-Free Sequences with Small Gaps

Xiaoyu He

arxiv:1501.04121 v1 · 2015-01-16 · math.NT · 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{TAMNJ3IZELKHY5BPD3AHRTK5VZ}

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	2026-05-18T00:40:08.660726Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9818d4ed1922d47c742f1ec078cd5dae5bc0c47232c32956b41281f2cd2b860d

Aliases

arxiv: 1501.04121 · arxiv_version: 1501.04121v1 · doi: 10.48550/arxiv.1501.04121 · pith_short_12: TAMNJ3IZELKH · pith_short_16: TAMNJ3IZELKHY5BP · pith_short_8: TAMNJ3IZ

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/TAMNJ3IZELKHY5BPD3AHRTK5VZ \
  | 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: 9818d4ed1922d47c742f1ec078cd5dae5bc0c47232c32956b41281f2cd2b860d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "934c45dcac8b9f8618a99033b2d5da6bced0275fc75667e75fcedd132fe9af44",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2015-01-16T21:54:30Z",
    "title_canon_sha256": "c776101ea5529c8522bc077fd0834b976dedcd42120b2f0900b4ec8a8617c7c0"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1501.04121",
    "kind": "arxiv",
    "version": 1
  }
}