Pith Number

pith:IMSMXQX3

pith:2007:IMSMXQX3WQA4QMUABLQPBJU3OJ

not attested not anchored not stored refs pending

Stochastic domination for iterated convolutions and catalytic majorization

Guillaume Aubrun (ICJ), Ion Nechita (ICJ)

arxiv:0707.0211 v2 · 2007-07-02 · quant-ph · math.PR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{IMSMXQX3WQA4QMUABLQPBJU3OJ}

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	2026-05-18T02:16:29.715918Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

4324cbc2fbb401c832800ae0f0a69b7253ef5ec6c9691111b2fce14234164b3a

Aliases

arxiv: 0707.0211 · arxiv_version: 0707.0211v2 · doi: 10.48550/arxiv.0707.0211 · pith_short_12: IMSMXQX3WQA4 · pith_short_16: IMSMXQX3WQA4QMUA · pith_short_8: IMSMXQX3

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/IMSMXQX3WQA4QMUABLQPBJU3OJ \
  | 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: 4324cbc2fbb401c832800ae0f0a69b7253ef5ec6c9691111b2fce14234164b3a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "97393e0149309617006d4b396636eb8d99ca44bf31718a3f5899f8935fabe991",
    "cross_cats_sorted": [
      "math.PR"
    ],
    "license": "",
    "primary_cat": "quant-ph",
    "submitted_at": "2007-07-02T12:44:14Z",
    "title_canon_sha256": "db537dee6961871c086828faac694cd9f605c778d20640225f564724dcceffab"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0707.0211",
    "kind": "arxiv",
    "version": 2
  }
}