Pith Number

pith:4OUATUQJ

pith:2026:4OUATUQJSSZGVP5ONDAARU5HZT

not attested not anchored not stored refs pending

A Near-Optimal Lower Bound for Prefix-Matrix Factorizations

David P. Woodruff, Honghao Lin, Vahab Mirrokni

arxiv:2608.08238 v1 · 2026-08-06 · cs.DS

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{4OUATUQJSSZGVP5ONDAARU5HZT}

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	2026-08-11T01:22:05.850993Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e3a809d20994b26abfae68c008d3a7ccc6f54f7cc99003fb986137014aba7e25

Aliases

arxiv: 2608.08238 · arxiv_version: 2608.08238v1 · doi: 10.48550/arxiv.2608.08238 · pith_short_12: 4OUATUQJSSZG · pith_short_16: 4OUATUQJSSZGVP5O · pith_short_8: 4OUATUQJ

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/4OUATUQJSSZGVP5ONDAARU5HZT \
  | 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: e3a809d20994b26abfae68c008d3a7ccc6f54f7cc99003fb986137014aba7e25

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "91de74cb41f9111b48bc6dc8a269b82aeb344bd99cf43cd62eec3f0596e52164",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.DS",
    "submitted_at": "2026-08-06T17:46:47Z",
    "title_canon_sha256": "2abd81dc98c3851b2294b964f8c5f6d650bf393c194f5b2d0100e420d1f49fb8"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2608.08238",
    "kind": "arxiv",
    "version": 1
  }
}