Pith Number

pith:ATGNCM7Y

pith:2012:ATGNCM7YE4LV2ZC73YZO7G4KAC

not attested not anchored not stored refs pending

Ricci-quadratic homogeneous Randers spaces

ShaoQiang Deng, Zhiguang Hu

arxiv:1207.1786 v1 · 2012-07-07 · 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{ATGNCM7YE4LV2ZC73YZO7G4KAC}

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	2026-05-18T03:51:34.679537Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

04ccd133f827175d645fde32ef9b8a00832fdbbeb47b52f7c29ff5f628eda8dc

Aliases

arxiv: 1207.1786 · arxiv_version: 1207.1786v1 · doi: 10.48550/arxiv.1207.1786 · pith_short_12: ATGNCM7YE4LV · pith_short_16: ATGNCM7YE4LV2ZC7 · pith_short_8: ATGNCM7Y

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/ATGNCM7YE4LV2ZC73YZO7G4KAC \
  | 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: 04ccd133f827175d645fde32ef9b8a00832fdbbeb47b52f7c29ff5f628eda8dc

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0824cd16d0700421c145a5bb5f32dd26f6b809abb3f83f709e7e5b3d50d0db3f",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2012-07-07T11:15:47Z",
    "title_canon_sha256": "fc0ac713379c5f34d048cf387ab15f4a882c2b7677764f6825e32d1010429765"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1207.1786",
    "kind": "arxiv",
    "version": 1
  }
}