Pith Number

pith:TRCVHU6J

pith:2016:TRCVHU6JU3ZKMOCAWAE3ZTEKGI

not attested not anchored not stored refs pending

Axioms of the Analytic Hierarchy Process (AHP) and its Generalization to Dependence and Feedback: The Analytic Network Process (ANP)

Konrad Ku{\l}akowski, Thomas Saaty

arxiv:1605.05777 v2 · 2016-05-18 · cs.DM

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{TRCVHU6JU3ZKMOCAWAE3ZTEKGI}

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	2026-05-18T01:12:01.318141Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9c4553d3c9a6f2a63840b009bccc8a322065ccc383c80772eda9abb09d25889e

Aliases

arxiv: 1605.05777 · arxiv_version: 1605.05777v2 · doi: 10.48550/arxiv.1605.05777 · pith_short_12: TRCVHU6JU3ZK · pith_short_16: TRCVHU6JU3ZKMOCA · pith_short_8: TRCVHU6J

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/TRCVHU6JU3ZKMOCAWAE3ZTEKGI \
  | 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: 9c4553d3c9a6f2a63840b009bccc8a322065ccc383c80772eda9abb09d25889e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "25d2bbbd217548506e4f7eb241a891fed00aac13fe5cee52cdff38e6da82e8ed",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.DM",
    "submitted_at": "2016-05-18T22:22:59Z",
    "title_canon_sha256": "fbba6a3f94db419d18f411db244abbe6e3fded3896788b4c5f854e1cafdf3891"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1605.05777",
    "kind": "arxiv",
    "version": 2
  }
}