Pith Number

pith:FO3CU6VU

pith:2025:FO3CU6VUJBJJOFKMRQK7MGY7FI

not attested not anchored not stored refs pending

Neural Expectation Operators

Qian Qi

arxiv:2507.10607 v1 · 2025-07-13 · math.PR · cs.AI · cs.LG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{FO3CU6VUJBJJOFKMRQK7MGY7FI}

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	2026-07-05T11:36:57.406235Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2bb62a7ab4485297154c8c15f61b1f2a13056a4363853d31c01be3ab5c8b91ec

Aliases

arxiv: 2507.10607 · arxiv_version: 2507.10607v1 · doi: 10.48550/arxiv.2507.10607 · pith_short_12: FO3CU6VUJBJJ · pith_short_16: FO3CU6VUJBJJOFKM · pith_short_8: FO3CU6VU

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/FO3CU6VUJBJJOFKMRQK7MGY7FI \
  | 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: 2bb62a7ab4485297154c8c15f61b1f2a13056a4363853d31c01be3ab5c8b91ec

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "cd3c4d1b1a90de2920d89ee297b20fa384c15633cc4ba2f3a7de52aeaa54f455",
    "cross_cats_sorted": [
      "cs.AI",
      "cs.LG"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2025-07-13T06:19:28Z",
    "title_canon_sha256": "b8aa60130aff554cbb70e3544e4f2effcd6636becf11d00e3e57d2cbb7e5f6dd"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2507.10607",
    "kind": "arxiv",
    "version": 1
  }
}