Pith Number

pith:6KJHIWD2

pith:2021:6KJHIWD2Q5JICDGTDVHYA7EX2X

not attested not anchored not stored refs pending

A Generalized Cross Ratio

Michael R. Pilla

arxiv:2106.10570 v1 · 2021-06-19 · math.CV

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{6KJHIWD2Q5JICDGTDVHYA7EX2X}

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	2026-06-24T01:14:54.627373Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f29274587a8752810cd31d4f807c97d5e221c4bac5dddf8921e0716fa2868232

Aliases

arxiv: 2106.10570 · arxiv_version: 2106.10570v1 · doi: 10.48550/arxiv.2106.10570 · pith_short_12: 6KJHIWD2Q5JI · pith_short_16: 6KJHIWD2Q5JICDGT · pith_short_8: 6KJHIWD2

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/6KJHIWD2Q5JICDGTDVHYA7EX2X \
  | 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: f29274587a8752810cd31d4f807c97d5e221c4bac5dddf8921e0716fa2868232

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9ce730b6a3bc931c6ed0ab86b4aa505268bc93aa4f68938f34b578e56fc2c48f",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.CV",
    "submitted_at": "2021-06-19T20:59:01Z",
    "title_canon_sha256": "47f8a656ece5d200363f4907d49c1539a277cbaae28181aac16e653d44e0149e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2106.10570",
    "kind": "arxiv",
    "version": 1
  }
}