Pith Number

pith:ZCLNN3G4

pith:2016:ZCLNN3G4CRP3YW542MYOKYPZW2

not attested not anchored not stored refs pending

Existence of tangent lines to Carnot-Carath\'eodory geodesics

Alessandro Pigati, Davide Vittone, Roberto Monti

arxiv:1609.07261 v2 · 2016-09-23 · math.OC · 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{ZCLNN3G4CRP3YW542MYOKYPZW2}

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	2026-05-18T00:30:55.416794Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c896d6ecdc145fbc5bbcd330e561f9b69f635590fecf004fd984361285895b34

Aliases

arxiv: 1609.07261 · arxiv_version: 1609.07261v2 · doi: 10.48550/arxiv.1609.07261 · pith_short_12: ZCLNN3G4CRP3 · pith_short_16: ZCLNN3G4CRP3YW54 · pith_short_8: ZCLNN3G4

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/ZCLNN3G4CRP3YW542MYOKYPZW2 \
  | 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: c896d6ecdc145fbc5bbcd330e561f9b69f635590fecf004fd984361285895b34

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4dcd383c5ff0e0ed5c519791ac8525a8646da3e0499476c5b5f3128096075b0a",
    "cross_cats_sorted": [
      "math.MG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OC",
    "submitted_at": "2016-09-23T07:51:26Z",
    "title_canon_sha256": "32c2e8b06032d734bd5e40927264bc23831ffd10dba4b59081f4a30192d41073"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1609.07261",
    "kind": "arxiv",
    "version": 2
  }
}