Pith Number

pith:V4T3YJRA

pith:2016:V4T3YJRAL5XDSCTWSYHQ4E5PTD

not attested not anchored not stored refs pending

Methods of tropical optimization in rating alternatives based on pairwise comparisons

Nikolai Krivulin

arxiv:1608.02666 v2 · 2016-08-09 · 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{V4T3YJRAL5XDSCTWSYHQ4E5PTD}

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	2026-05-18T00:38:09.359114Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

af27bc26205f6e390a76960f0e13af98ddc5f1316161ba70340a47fb25b280c0

Aliases

arxiv: 1608.02666 · arxiv_version: 1608.02666v2 · doi: 10.48550/arxiv.1608.02666 · pith_short_12: V4T3YJRAL5XD · pith_short_16: V4T3YJRAL5XDSCTW · pith_short_8: V4T3YJRA

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/V4T3YJRAL5XDSCTWSYHQ4E5PTD \
  | 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: af27bc26205f6e390a76960f0e13af98ddc5f1316161ba70340a47fb25b280c0

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f9c6b8f3d6704ec2fdd614ac3fd0ca3f10fc3828aed1c043d59de6206f314ca6",
    "cross_cats_sorted": [
      "cs.SY"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OC",
    "submitted_at": "2016-08-09T00:28:57Z",
    "title_canon_sha256": "1195fd323a89f5c0dff61399f98d9147a2f6ee543bc25a0a7786746c080927db"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1608.02666",
    "kind": "arxiv",
    "version": 2
  }
}