Pith Number

pith:CY3CDQSP

pith:2014:CY3CDQSPKLMY6YD4SVLB3QTT66

not attested not anchored not stored refs pending

Beyond traditional Curvature-Dimension I: new model spaces for isoperimetric and concentration inequalities in negative dimension

Emanuel Milman

arxiv:1409.4109 v4 · 2014-09-14 · math.DG · math.FA · math.MG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{CY3CDQSPKLMY6YD4SVLB3QTT66}

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	2026-05-18T00:54:48.364907Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

163621c24f52d98f607c95561dc273f7866ad837400603dbe13c8e24a92eefe7

Aliases

arxiv: 1409.4109 · arxiv_version: 1409.4109v4 · doi: 10.48550/arxiv.1409.4109 · pith_short_12: CY3CDQSPKLMY · pith_short_16: CY3CDQSPKLMY6YD4 · pith_short_8: CY3CDQSP

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/CY3CDQSPKLMY6YD4SVLB3QTT66 \
  | 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: 163621c24f52d98f607c95561dc273f7866ad837400603dbe13c8e24a92eefe7

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "77b8e8e66c4af397f9eb0aa4c05f7f82c91fd35adf75bed0853b248991382bd5",
    "cross_cats_sorted": [
      "math.FA",
      "math.MG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2014-09-14T21:38:46Z",
    "title_canon_sha256": "e1d403380e7bbbf5f34b0ced4c39fea2ff0f20da61046fc877537322def6d153"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1409.4109",
    "kind": "arxiv",
    "version": 4
  }
}