Pith Number

pith:77DGOBVC

pith:2010:77DGOBVCHLGZXERFCQTXWYQRMS

not attested not anchored not stored refs pending

Smooth paths of conditional expectations

Esteban Andruchow, Gabriel Larotonda

arxiv:1010.1045 v1 · 2010-10-06 · 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{77DGOBVCHLGZXERFCQTXWYQRMS}

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	2026-05-18T04:39:49.925526Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ffc66706a23acd9b922514277b6211648398f39d9428605d4a4d04c75ef15a8f

Aliases

arxiv: 1010.1045 · arxiv_version: 1010.1045v1 · doi: 10.48550/arxiv.1010.1045 · pith_short_12: 77DGOBVCHLGZ · pith_short_16: 77DGOBVCHLGZXERF · pith_short_8: 77DGOBVC

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/77DGOBVCHLGZXERFCQTXWYQRMS \
  | 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: ffc66706a23acd9b922514277b6211648398f39d9428605d4a4d04c75ef15a8f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8cdfba237207d191fb0d9e087465d52f81c628411df58a579b9b0c1f093c616b",
    "cross_cats_sorted": [
      "math.FA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OA",
    "submitted_at": "2010-10-06T01:03:51Z",
    "title_canon_sha256": "5876433130f529360b4e90cf1c98158bb665bb9063ed0582a0ab4c16ee13a41a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1010.1045",
    "kind": "arxiv",
    "version": 1
  }
}