Pith Number

pith:V3IO674M

pith:2009:V3IO674MBAOBV7RTCENW6XZYZ4

not attested not anchored not stored refs pending

Phase-space analysis and pseudodifferential calculus on the Heisenberg group

Clotilde Fermanian-Kammerer (LAMA), Hajer Bahouri, Isabelle Gallagher (IMJ)

arxiv:0904.4746 v2 · 2009-04-30 · 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{V3IO674MBAOBV7RTCENW6XZYZ4}

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	2026-05-18T03:32:17.338922Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

aed0ef7f8c081c1afe33111b6f5f38cf3f9d964cde27fd419cc1f0c5b78b5a8a

Aliases

arxiv: 0904.4746 · arxiv_version: 0904.4746v2 · doi: 10.48550/arxiv.0904.4746 · pith_short_12: V3IO674MBAOB · pith_short_16: V3IO674MBAOBV7RT · pith_short_8: V3IO674M

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/V3IO674MBAOBV7RTCENW6XZYZ4 \
  | 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: aed0ef7f8c081c1afe33111b6f5f38cf3f9d964cde27fd419cc1f0c5b78b5a8a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "13006fc2ca778e6c97fa25777bb2d152fe84177b660c172f4f896ea3d55d6a98",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2009-04-30T06:19:38Z",
    "title_canon_sha256": "301be1c305afdb0d1293b0739ddcc9a5f1dc00722fca1185462330ef9ba3d531"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0904.4746",
    "kind": "arxiv",
    "version": 2
  }
}