Pith Number

pith:ZQ2OE2JN

pith:2015:ZQ2OE2JNEGED7GOPL7F56Z7ZA6

not attested not anchored not stored refs pending

The emergence of 4-cycles in polynomial maps over the extended integers

Andrew Best, Benjamin L. Weiss, Jasmine Powell, Patrick Dynes, Steven J. Miller

arxiv:1507.03597 v1 · 2015-07-13 · 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{ZQ2OE2JNEGED7GOPL7F56Z7ZA6}

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	2026-05-18T01:36:57.853864Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

cc34e2692d21883f99cf5fcbdf67f907a2f1291d8b01eb649ebe80e767051cfa

Aliases

arxiv: 1507.03597 · arxiv_version: 1507.03597v1 · doi: 10.48550/arxiv.1507.03597 · pith_short_12: ZQ2OE2JNEGED · pith_short_16: ZQ2OE2JNEGED7GOP · pith_short_8: ZQ2OE2JN

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/ZQ2OE2JNEGED7GOPL7F56Z7ZA6 \
  | 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: cc34e2692d21883f99cf5fcbdf67f907a2f1291d8b01eb649ebe80e767051cfa

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "edca638c95caf534134f5e5ebbbc35ad26f54da64f9fd07206de2b344ae5d1fa",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2015-07-13T20:01:26Z",
    "title_canon_sha256": "c7398352aeda0124dd60f5d91ef439f8c79ffc1c8273b1a34f0c0b219ebf6d12"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1507.03597",
    "kind": "arxiv",
    "version": 1
  }
}