Pith Number

pith:OBKNN57I

pith:2026:OBKNN57IVEMLN4KQBBZOXN5AQE

not attested not anchored not stored refs pending

Multi-Vector Embeddings are Provably More Expressive than Single Vector Embeddings

Rajesh Jayaram

arxiv:2606.23475 v1 · 2026-06-22 · cs.DS · cs.IR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{OBKNN57IVEMLN4KQBBZOXN5AQE}

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	2026-06-23T03:14:20.897390Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7054d6f7e8a918b6f1500872ebb7a08106230f3cea9933517f0cd3dec8702e9e

Aliases

arxiv: 2606.23475 · arxiv_version: 2606.23475v1 · doi: 10.48550/arxiv.2606.23475 · pith_short_12: OBKNN57IVEML · pith_short_16: OBKNN57IVEMLN4KQ · pith_short_8: OBKNN57I

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/OBKNN57IVEMLN4KQBBZOXN5AQE \
  | 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: 7054d6f7e8a918b6f1500872ebb7a08106230f3cea9933517f0cd3dec8702e9e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "31e6ed747b6ecbc20f38adb16aa82ea35ea38e5e05450e0645c0b77e5e09e0a2",
    "cross_cats_sorted": [
      "cs.IR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.DS",
    "submitted_at": "2026-06-22T15:22:05Z",
    "title_canon_sha256": "9d1c98a99b9a6861c8a5a7f66d7d589375f4385368a8c53501c8ebb06fdb13e6"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.23475",
    "kind": "arxiv",
    "version": 1
  }
}