Pith Number

pith:W5NO72AW

pith:2026:W5NO72AWLSVAFLIUT2UFDSX3X7

not attested not anchored not stored refs pending

Eigenvalue optimization via a first-variation formula

Denis Vinokurov

arxiv:2606.31869 v1 · 2026-06-30 · math.SP · math.FA · math.OC

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{W5NO72AWLSVAFLIUT2UFDSX3X7}

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	2026-07-01T01:18:18.038622Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b75aefe8165caa02ad149ea851cafbbfdff8d0183fec2b3f5ea86698e6980449

Aliases

arxiv: 2606.31869 · arxiv_version: 2606.31869v1 · doi: 10.48550/arxiv.2606.31869 · pith_short_12: W5NO72AWLSVA · pith_short_16: W5NO72AWLSVAFLIU · pith_short_8: W5NO72AW

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/W5NO72AWLSVAFLIUT2UFDSX3X7 \
  | 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: b75aefe8165caa02ad149ea851cafbbfdff8d0183fec2b3f5ea86698e6980449

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "86d40e849e55df60f33418449437f40e8c013268e6c2f7b92560b4d5d912c091",
    "cross_cats_sorted": [
      "math.FA",
      "math.OC"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.SP",
    "submitted_at": "2026-06-30T15:55:54Z",
    "title_canon_sha256": "df9d5797aee78f375f16e717f15c12e1ed9dd59e369f196cc5418b01bfa72ac5"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.31869",
    "kind": "arxiv",
    "version": 1
  }
}