Pith Number

pith:ADB4DRSU

pith:2012:ADB4DRSUE4M2CFXZKHQ3YO3GBV

not attested not anchored not stored refs pending

BMO estimates for nonvariational operators with discontinuous coefficients structured on Hormander's vector fields on Carnot groups

Marco Bramanti, Maria Stella Fanciullo

arxiv:1209.3601 v1 · 2012-09-17 · 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{ADB4DRSUE4M2CFXZKHQ3YO3GBV}

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	2026-05-18T03:45:30.503698Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

00c3c1c6542719a116f951e1bc3b660d4a64fcc4eddaedd7659b9670d0e6a45b

Aliases

arxiv: 1209.3601 · arxiv_version: 1209.3601v1 · doi: 10.48550/arxiv.1209.3601 · pith_short_12: ADB4DRSUE4M2 · pith_short_16: ADB4DRSUE4M2CFXZ · pith_short_8: ADB4DRSU

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/ADB4DRSUE4M2CFXZKHQ3YO3GBV \
  | 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: 00c3c1c6542719a116f951e1bc3b660d4a64fcc4eddaedd7659b9670d0e6a45b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "271559d97abba141a27fc33aefd7f304be49caa21ca51b00ea10019c35c5eb38",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2012-09-17T09:14:31Z",
    "title_canon_sha256": "73aee8c3c4be737d6ebd2185db8267e25e991c4be2cdb7dd6ac76199a80b7f63"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1209.3601",
    "kind": "arxiv",
    "version": 1
  }
}