Pith Number

pith:BYBDUENU

pith:2024:BYBDUENU3YLGMG6OGHRK2HMV3K

not attested not anchored not stored refs pending

Approximate Fiber Product: A Preliminary Algebraic-Geometric Perspective on Multimodal Embedding Alignment

Dongfang Zhao

arxiv:2412.00373 v1 · 2024-11-30 · cs.LG · cs.AI · math.AG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{BYBDUENU3YLGMG6OGHRK2HMV3K}

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	2026-07-05T09:42:40.307837Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0e023a11b4de16661bce31e2ad1d95da82850689025b63e9521700a4700c316b

Aliases

arxiv: 2412.00373 · arxiv_version: 2412.00373v1 · doi: 10.48550/arxiv.2412.00373 · pith_short_12: BYBDUENU3YLG · pith_short_16: BYBDUENU3YLGMG6O · pith_short_8: BYBDUENU

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/BYBDUENU3YLGMG6OGHRK2HMV3K \
  | 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: 0e023a11b4de16661bce31e2ad1d95da82850689025b63e9521700a4700c316b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "949f13d2328196f6c98f4812604ffc78743538f4adf891aaae387790612b7e57",
    "cross_cats_sorted": [
      "cs.AI",
      "math.AG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.LG",
    "submitted_at": "2024-11-30T06:45:13Z",
    "title_canon_sha256": "3d687e8653dce43a806cc3908adcbeebf2cc5f9e70309558d483e5aa2ed0e254"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2412.00373",
    "kind": "arxiv",
    "version": 1
  }
}