Pith Number

pith:QPKEHCZU

pith:2018:QPKEHCZU7BXT5SJOM2G7BUUIF6

not attested not anchored not stored refs pending

Using tropical optimization techniques in bi-criteria decision problems

Nikolai Krivulin

arxiv:1810.08662 v2 · 2018-10-19 · 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{QPKEHCZU7BXT5SJOM2G7BUUIF6}

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	2026-05-17T23:49:50.691503Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

83d4438b34f86f3ec92e668df0d2882f8ae27f3da92011477dd2ed1de427b836

Aliases

arxiv: 1810.08662 · arxiv_version: 1810.08662v2 · doi: 10.48550/arxiv.1810.08662 · pith_short_12: QPKEHCZU7BXT · pith_short_16: QPKEHCZU7BXT5SJO · pith_short_8: QPKEHCZU

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/QPKEHCZU7BXT5SJOM2G7BUUIF6 \
  | 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: 83d4438b34f86f3ec92e668df0d2882f8ae27f3da92011477dd2ed1de427b836

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7317d2df673147e4e8f625a6f3647bea26da08763ada11c36343f13cdbdf9e96",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OC",
    "submitted_at": "2018-10-19T19:27:21Z",
    "title_canon_sha256": "94ca6fe05e815e5205c65e31cc47fd64f6f1fc44a36a796a5e54b725d544a5e0"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1810.08662",
    "kind": "arxiv",
    "version": 2
  }
}