Pith Number

pith:NQPZDBBL

pith:2006:NQPZDBBLDNOUG47TBFO5TTDO34

not attested not anchored not stored refs pending

On the role of abnormal minimizers in sub-Riemannian geometry

Bernard Bonnard (IMB), Emmanuel Tr\'elat (IMB)

arxiv:math/0607426 v1 · 2006-07-18 · 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{NQPZDBBLDNOUG47TBFO5TTDO34}

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	2026-05-18T01:08:50.018913Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6c1f91842b1b5d4373f3095dd9cc6edf00f85ad5e3d17a6eb5f9be8ceb2a0857

Aliases

arxiv: math/0607426 · arxiv_version: math/0607426v1 · doi: 10.48550/arxiv.math/0607426 · pith_short_12: NQPZDBBLDNOU · pith_short_16: NQPZDBBLDNOUG47T · pith_short_8: NQPZDBBL

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/NQPZDBBLDNOUG47TBFO5TTDO34 \
  | 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: 6c1f91842b1b5d4373f3095dd9cc6edf00f85ad5e3d17a6eb5f9be8ceb2a0857

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5316752c904488139bb02dedb7722ebfcf52dd5d6c178798580491eba94a165d",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "math.OC",
    "submitted_at": "2006-07-18T15:31:18Z",
    "title_canon_sha256": "1f6cc7bd22ea2d988cd279f0c5f082ad9f31028d97f6a360d17e4a1794128622"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0607426",
    "kind": "arxiv",
    "version": 1
  }
}