Pith Number

pith:UPNETH5A

pith:2014:UPNETH5AYD4TN2XX73YZIE7RZQ

not attested not anchored not stored refs pending

Comparison theorems for conjugate points in sub-Riemannian geometry

Davide Barilari, Luca Rizzi

arxiv:1401.3193 v5 · 2014-01-14 · 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{UPNETH5AYD4TN2XX73YZIE7RZQ}

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	2026-05-18T01:14:59.081571Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a3da499fa0c0f936eaf7fef19413f1cc2d716914ca837af848c0c228620e32cb

Aliases

arxiv: 1401.3193 · arxiv_version: 1401.3193v5 · doi: 10.48550/arxiv.1401.3193 · pith_short_12: UPNETH5AYD4T · pith_short_16: UPNETH5AYD4TN2XX · pith_short_8: UPNETH5A

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/UPNETH5AYD4TN2XX73YZIE7RZQ \
  | 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: a3da499fa0c0f936eaf7fef19413f1cc2d716914ca837af848c0c228620e32cb

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2030df3aafd4feb8038c803df5d9c8c380cc399c4f4fb3f3ab4c26f8a964c96d",
    "cross_cats_sorted": [
      "math.MG",
      "math.OC"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2014-01-14T14:22:02Z",
    "title_canon_sha256": "37404d393ebb3e91d4fcffe76f43492c89e6cd76570d9f187e3de26852aa32a8"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1401.3193",
    "kind": "arxiv",
    "version": 5
  }
}