Pith Number

pith:X4V7XEZU

pith:2025:X4V7XEZU3OLF3TLOJ5L3ODFJFE

not attested not anchored not stored refs pending

Critical singular problems in Carnot groups

Eugenio Vecchi, Mattia Galeotti, Stefano Biagi

arxiv:2506.07521 v1 · 2025-06-09 · math.AP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{X4V7XEZU3OLF3TLOJ5L3ODFJFE}

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

Critical concave-convex problems in Carnot groups

Receipt and verification

First computed	2026-07-05T11:18:28.774048Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

bf2bfb9334db965dcd6e4f57b70ca92925c43460b5ed194a9390312806134fe9

Aliases

arxiv: 2506.07521 · arxiv_version: 2506.07521v1 · doi: 10.48550/arxiv.2506.07521 · pith_short_12: X4V7XEZU3OLF · pith_short_16: X4V7XEZU3OLF3TLO · pith_short_8: X4V7XEZU

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/X4V7XEZU3OLF3TLOJ5L3ODFJFE \
  | 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: bf2bfb9334db965dcd6e4f57b70ca92925c43460b5ed194a9390312806134fe9

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c84d8511fe191d055aceb11193de6675f2d59bac29946bf74dd80612684b3792",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2025-06-09T07:58:32Z",
    "title_canon_sha256": "3efe553ffe3f86354a7ab5253ddb5cf46da9554e19f3efb0ae3fcaf1dba74f53"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2506.07521",
    "kind": "arxiv",
    "version": 1
  }
}