Pith Number

pith:24MUD2CE

pith:2016:24MUD2CE6BQ7NFNZO3K2NOF735

not attested not anchored not stored refs pending

Conditionally expectations and martingales in noncommutative $L_p$-spaces associated with center-valued traces

Farrukh Mukhamedov, Inomjon Ganiev

arxiv:1603.08621 v1 · 2016-03-29 · math.OA · math.FA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{24MUD2CE6BQ7NFNZO3K2NOF735}

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	2026-05-18T00:38:11.510370Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d71941e844f061f695b976d5a6b8bfdf78c3bae8850e2cd5e6a887787459197f

Aliases

arxiv: 1603.08621 · arxiv_version: 1603.08621v1 · doi: 10.48550/arxiv.1603.08621 · pith_short_12: 24MUD2CE6BQ7 · pith_short_16: 24MUD2CE6BQ7NFNZ · pith_short_8: 24MUD2CE

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/24MUD2CE6BQ7NFNZO3K2NOF735 \
  | 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: d71941e844f061f695b976d5a6b8bfdf78c3bae8850e2cd5e6a887787459197f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f5d04ce00087e8e4a989521fc6e7362d92333b25cfaf30b77ad75e10fd969ed3",
    "cross_cats_sorted": [
      "math.FA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OA",
    "submitted_at": "2016-03-29T03:02:14Z",
    "title_canon_sha256": "83a5ddea7eb343b2bbf8337d9e49f20ddfd2d8bea9c42259121b4872bd06a651"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1603.08621",
    "kind": "arxiv",
    "version": 1
  }
}