Pith Number

pith:AHZXFCUF

pith:2015:AHZXFCUFB6GXL63MJWK35BPRQH

not attested not anchored not stored refs pending

Twisted patterns in large subsets of $\mathbb{Z}^N$

Kamil Bulinski, Michael Bj\"orklund

arxiv:1512.01719 v1 · 2015-12-06 · math.DS · math.CO · 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{AHZXFCUFB6GXL63MJWK35BPRQH}

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	2026-05-18T01:25:10.535063Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

01f3728a850f8d75fb6c4d95be85f181c6292ff3c6f2a2b6701dbc815fd8c80b

Aliases

arxiv: 1512.01719 · arxiv_version: 1512.01719v1 · doi: 10.48550/arxiv.1512.01719 · pith_short_12: AHZXFCUFB6GX · pith_short_16: AHZXFCUFB6GXL63M · pith_short_8: AHZXFCUF

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/AHZXFCUFB6GXL63MJWK35BPRQH \
  | 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: 01f3728a850f8d75fb6c4d95be85f181c6292ff3c6f2a2b6701dbc815fd8c80b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e04c32c9655f50b9e5f89634fe9e0922c74c8b36451d6dcd3037ce721683b8c3",
    "cross_cats_sorted": [
      "math.CO",
      "math.NT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2015-12-06T01:15:35Z",
    "title_canon_sha256": "5a6775c92cc9e15b2daa6b874b56c873ca4c6c4961e4c08995f03670e34e7398"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1512.01719",
    "kind": "arxiv",
    "version": 1
  }
}