Pith Number

pith:CD7Z3XGC

pith:2018:CD7Z3XGCNA3RGCYHAEHEZZWC2Y

not attested not anchored not stored refs pending

On the regularity of abnormal minimizers for rank $2$ sub-Riemannian structures

Dario Prandi, Davide Barilari, Fr\'ed\'eric Jean, Mario Sigalotti, Yacine Chitour

arxiv:1804.00971 v2 · 2018-04-03 · math.OC · math.DG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{CD7Z3XGCNA3RGCYHAEHEZZWC2Y}

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	2026-05-17T23:59:17.448127Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

10ff9ddcc26837130b07010e4ce6c2d6082a7560fecc08d465620ca38550df16

Aliases

arxiv: 1804.00971 · arxiv_version: 1804.00971v2 · doi: 10.48550/arxiv.1804.00971 · pith_short_12: CD7Z3XGCNA3R · pith_short_16: CD7Z3XGCNA3RGCYH · pith_short_8: CD7Z3XGC

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/CD7Z3XGCNA3RGCYHAEHEZZWC2Y \
  | 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: 10ff9ddcc26837130b07010e4ce6c2d6082a7560fecc08d465620ca38550df16

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "bdf7b77fd6f89deb5e616aeeacdca940b3e30e1be9d34019fde93f66ffce7888",
    "cross_cats_sorted": [
      "math.DG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OC",
    "submitted_at": "2018-04-03T14:12:03Z",
    "title_canon_sha256": "16221dde7da78f0df7567f866f6ee7d0ca6669277c87ae5d7949e5e04e5538f4"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1804.00971",
    "kind": "arxiv",
    "version": 2
  }
}