Pith Number

pith:OPFPCRGH

pith:2016:OPFPCRGH5ZQWXTACDYDXYUO6JH

not attested not anchored not stored refs pending

Sums of twisted circulants

Aaron Abrams, Henry Landau, James Pommersheim, Zeph Landau

arxiv:1607.05716 v1 · 2016-07-19 · math.PR · math.GR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{OPFPCRGH5ZQWXTACDYDXYUO6JH}

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	2026-05-18T01:10:46.196706Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

73caf144c7ee616bcc021e077c51de49c25123f9fa60cdaaad1398385737e9c2

Aliases

arxiv: 1607.05716 · arxiv_version: 1607.05716v1 · doi: 10.48550/arxiv.1607.05716 · pith_short_12: OPFPCRGH5ZQW · pith_short_16: OPFPCRGH5ZQWXTAC · pith_short_8: OPFPCRGH

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/OPFPCRGH5ZQWXTACDYDXYUO6JH \
  | 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: 73caf144c7ee616bcc021e077c51de49c25123f9fa60cdaaad1398385737e9c2

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d4cecbf7988ffa278a589ff999d1968738cd9022deb44d6130cf239eee944892",
    "cross_cats_sorted": [
      "math.GR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2016-07-19T19:57:46Z",
    "title_canon_sha256": "51a3d02c4b47979abe545fb1535696ef2fe40a5ae864a3efb2a042f8175cbd66"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1607.05716",
    "kind": "arxiv",
    "version": 1
  }
}