Pith Number

pith:52AKQ6KQ

pith:2013:52AKQ6KQKUMQLJ247Y74RAYBZO

not attested not anchored not stored refs pending

Extremal properties of tropical eigenvalues and solutions to tropical optimization problems

Nikolai Krivulin

arxiv:1311.0442 v2 · 2013-11-03 · math.OC · cs.SY

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{52AKQ6KQKUMQLJ247Y74RAYBZO}

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	2026-05-18T02:28:23.275421Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ee80a87950551905a75cfe3fc88301cbbb661b5044c4554dc65309a98cefd608

Aliases

arxiv: 1311.0442 · arxiv_version: 1311.0442v2 · doi: 10.48550/arxiv.1311.0442 · pith_short_12: 52AKQ6KQKUMQ · pith_short_16: 52AKQ6KQKUMQLJ24 · pith_short_8: 52AKQ6KQ

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/52AKQ6KQKUMQLJ247Y74RAYBZO \
  | 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: ee80a87950551905a75cfe3fc88301cbbb661b5044c4554dc65309a98cefd608

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "bd1d0ce4d8e4849ce4d2039ccc5f788fb043df71724a920d29898fac323014be",
    "cross_cats_sorted": [
      "cs.SY"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OC",
    "submitted_at": "2013-11-03T09:26:32Z",
    "title_canon_sha256": "cd9354d62533faa98c0e4ecbad04d41c6cc460f9e4454560e7a8313b02d10670"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1311.0442",
    "kind": "arxiv",
    "version": 2
  }
}