Pith Number

pith:ANBUFQKP

pith:2013:ANBUFQKP7S5GCJYXGGPOXEJC45

not attested not anchored not stored refs pending

Recurrence and non-uniformity of bracket polynomials

Matthew Tointon

arxiv:1309.6470 v2 · 2013-09-25 · math.NT · math.CO · math.DS

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{ANBUFQKP7S5GCJYXGGPOXEJC45}

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	2026-05-18T02:41:58.353161Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

034342c14ffcba612717319eeb9122e768d2c6911f531b53642deb3defcfbdfe

Aliases

arxiv: 1309.6470 · arxiv_version: 1309.6470v2 · doi: 10.48550/arxiv.1309.6470 · pith_short_12: ANBUFQKP7S5G · pith_short_16: ANBUFQKP7S5GCJYX · pith_short_8: ANBUFQKP

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/ANBUFQKP7S5GCJYXGGPOXEJC45 \
  | 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: 034342c14ffcba612717319eeb9122e768d2c6911f531b53642deb3defcfbdfe

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "473d072462034669a1dc747f0e00776fbc474ea7307f43bb7ca490ef6c6f617c",
    "cross_cats_sorted": [
      "math.CO",
      "math.DS"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2013-09-25T11:41:44Z",
    "title_canon_sha256": "224fb5bd01f58b4ede9045f8838a2edea00b92e2658fb9926a690f3de26c981d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1309.6470",
    "kind": "arxiv",
    "version": 2
  }
}