Pith Number

pith:DEOCKSD5

pith:2012:DEOCKSD5OBIUWLR2QEOU3NZTNM

not attested not anchored not stored refs pending

A pseudo-differential calculus on graded Lie groups

Michael Ruzhansky, Veronique Fischer

arxiv:1209.2621 v2 · 2012-09-12 · math.FA · math.AP · math.RT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{DEOCKSD5OBIUWLR2QEOU3NZTNM}

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	2026-05-18T01:30:08.678894Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

191c25487d70514b2e3a811d4db7336b14ce83a6a911bfde0acf163e068a46b6

Aliases

arxiv: 1209.2621 · arxiv_version: 1209.2621v2 · doi: 10.48550/arxiv.1209.2621 · pith_short_12: DEOCKSD5OBIU · pith_short_16: DEOCKSD5OBIUWLR2 · pith_short_8: DEOCKSD5

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/DEOCKSD5OBIUWLR2QEOU3NZTNM \
  | 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: 191c25487d70514b2e3a811d4db7336b14ce83a6a911bfde0acf163e068a46b6

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "15b58358ed285fd1476df69bca0c08d08a973349f5554ed6170e85b3b0821b0b",
    "cross_cats_sorted": [
      "math.AP",
      "math.RT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2012-09-12T14:17:42Z",
    "title_canon_sha256": "374788dc915fcd4c8518d09648e643f82ef5b8def762b82bd0ec94f91b6fddb5"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1209.2621",
    "kind": "arxiv",
    "version": 2
  }
}