Pith Number

pith:RJDC4HPJ

pith:2019:RJDC4HPJI2LL3ED7S6QY5S3V3H

not attested not anchored not stored refs pending

Constant index expectation curvature for graphs or Riemannian manifolds

Oliver Knill

arxiv:1912.11315 v1 · 2019-12-24 · math.CO · cs.DM

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{RJDC4HPJI2LL3ED7S6QY5S3V3H}

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.

Cited by

1 paper in Pith

Elements of finite geometry I

Receipt and verification

First computed	2026-07-05T00:28:19.069362Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

8a462e1de94696bd907f97a18ecb75d9e3c74faa5ba09c70577f9a48acceafdd

Aliases

arxiv: 1912.11315 · arxiv_version: 1912.11315v1 · doi: 10.48550/arxiv.1912.11315 · pith_short_12: RJDC4HPJI2LL · pith_short_16: RJDC4HPJI2LL3ED7 · pith_short_8: RJDC4HPJ

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/RJDC4HPJI2LL3ED7S6QY5S3V3H \
  | 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: 8a462e1de94696bd907f97a18ecb75d9e3c74faa5ba09c70577f9a48acceafdd

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "462a2c2b739d6dd3f8e7c760bed45be8b09b0c72ee13466ef75f1c8d2397342e",
    "cross_cats_sorted": [
      "cs.DM"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2019-12-24T12:20:58Z",
    "title_canon_sha256": "1da06c5f35cdf374c9639fcea2d2f7304fc1d19becdb944fa4f4570e86e1dbf9"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1912.11315",
    "kind": "arxiv",
    "version": 1
  }
}