Pith Number

pith:ORJRH25A

pith:2018:ORJRH25AIBOKQG2QXIDYY7UPXN

not attested not anchored not stored refs pending

Volume of small balls and sub-Riemannian curvature in 3D contact manifolds

Antonio Lerario, Davide Barilari, Ivan Beschastnyi

arxiv:1802.10155 v2 · 2018-02-27 · math.DG · math.MG · math.OC

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{ORJRH25AIBOKQG2QXIDYY7UPXN}

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

Representation Gap: Explaining the Unreasonable Effectiveness of Neural Networks from a Geometric Perspective

Receipt and verification

First computed	2026-05-17T23:59:17.609233Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

745313eba0405ca81b50ba078c7e8fbb71fdfba9c6bb887c19a0e37b512d0317

Aliases

arxiv: 1802.10155 · arxiv_version: 1802.10155v2 · doi: 10.48550/arxiv.1802.10155 · pith_short_12: ORJRH25AIBOK · pith_short_16: ORJRH25AIBOKQG2Q · pith_short_8: ORJRH25A

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/ORJRH25AIBOKQG2QXIDYY7UPXN \
  | 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: 745313eba0405ca81b50ba078c7e8fbb71fdfba9c6bb887c19a0e37b512d0317

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3206eb2b0798c1b514fd23a92b6dff22101697d764cd10531280baabe4f34355",
    "cross_cats_sorted": [
      "math.MG",
      "math.OC"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2018-02-27T20:37:39Z",
    "title_canon_sha256": "14ba6500ab9b8756f1d852378271aa8a70fa0bdcad793ebe2ed11f123f0aea1d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1802.10155",
    "kind": "arxiv",
    "version": 2
  }
}