Pith Number

pith:ONYPYSNJ

pith:2019:ONYPYSNJYV4EFLIOPNLSBTDRLC

not attested not anchored not stored refs pending

The Quasi Curvature-Dimension Condition with applications to sub-Riemannian manifolds

Emanuel Milman

arxiv:1908.01513 v5 · 2019-08-05 · math.FA · math.DG · math.MG · math.SP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{ONYPYSNJYV4EFLIOPNLSBTDRLC}

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	2026-07-05T01:35:43.564400Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7370fc49a9c57842ad0e7b5720cc71588eee9bc698f696c962aec35e5e396266

Aliases

arxiv: 1908.01513 · arxiv_version: 1908.01513v5 · doi: 10.48550/arxiv.1908.01513 · pith_short_12: ONYPYSNJYV4E · pith_short_16: ONYPYSNJYV4EFLIO · pith_short_8: ONYPYSNJ

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/ONYPYSNJYV4EFLIOPNLSBTDRLC \
  | 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: 7370fc49a9c57842ad0e7b5720cc71588eee9bc698f696c962aec35e5e396266

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "fe67b08cc5b81b8a20563c16c288999e00e55c077c4c7336c8cd9fe958f27bbb",
    "cross_cats_sorted": [
      "math.DG",
      "math.MG",
      "math.SP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2019-08-05T08:24:40Z",
    "title_canon_sha256": "af919e8906b464d5300f6d128b0a886ec9b7f678314d697f47b178765912176c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1908.01513",
    "kind": "arxiv",
    "version": 5
  }
}