Pith Number

pith:2AIKZ2ZJ

pith:2020:2AIKZ2ZJE3EURGPRCIQ5HIVWTC

not attested not anchored not stored refs pending

On index expectation curvature for manifolds

Oliver Knill

arxiv:2001.06925 v1 · 2020-01-20 · math.DG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{2AIKZ2ZJE3EURGPRCIQ5HIVWTC}

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	2026-07-05T00:34:25.867548Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d010aceb2926c94899f11221d3a2b698ad23efa306e4f917ab59208a20bd915c

Aliases

arxiv: 2001.06925 · arxiv_version: 2001.06925v1 · doi: 10.48550/arxiv.2001.06925 · pith_short_12: 2AIKZ2ZJE3EU · pith_short_16: 2AIKZ2ZJE3EURGPR · pith_short_8: 2AIKZ2ZJ

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/2AIKZ2ZJE3EURGPRCIQ5HIVWTC \
  | 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: d010aceb2926c94899f11221d3a2b698ad23efa306e4f917ab59208a20bd915c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "27b73c91cd8e7b0ea46a8faa5b45d27c3c19519637b4881cc4c492a3cc1cd769",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2020-01-20T00:46:43Z",
    "title_canon_sha256": "b299d924efc98a2500f5856eb67265cf0354a044d9271d6c60a5713f617ae3ba"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2001.06925",
    "kind": "arxiv",
    "version": 1
  }
}