Pith Number

pith:XAQF7D2C

pith:2015:XAQF7D2CHGVFUDJOCKFCQSPMNY

not attested not anchored not stored refs pending

Characterization of non-constant lower bound of Ricci curvature via entropy inequality on Wasserstein space

Bo Wu, Jinghai Shao

arxiv:1507.07995 v1 · 2015-07-29 · math.PR

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

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	2026-05-18T01:36:08.699691Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b8205f8f4239aa5a0d2e128a2849ec6e39cdbf8d977560690b04d489c04416ac

Aliases

arxiv: 1507.07995 · arxiv_version: 1507.07995v1 · doi: 10.48550/arxiv.1507.07995 · pith_short_12: XAQF7D2CHGVF · pith_short_16: XAQF7D2CHGVFUDJO · pith_short_8: XAQF7D2C

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/XAQF7D2CHGVFUDJOCKFCQSPMNY \
  | 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: b8205f8f4239aa5a0d2e128a2849ec6e39cdbf8d977560690b04d489c04416ac

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6a91e6b2d79ef2700f6733e4537234b48b6af68861ee5501f98e73c1c71bd4a4",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2015-07-29T00:36:11Z",
    "title_canon_sha256": "7815ada67d38a5b8b5b7105aeaff1b16141ca822bdbac659fe87ed905c79d0a7"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1507.07995",
    "kind": "arxiv",
    "version": 1
  }
}