Pith Number

pith:MK5MIAXC

pith:2017:MK5MIAXCARXEEPAZ5GDF4TQ4G5

not attested not anchored not stored refs pending

The (logarithmic) least squares optimality of the arithmetic (geometric) mean of weight vectors calculated from all spanning trees for incomplete additive (multiplicative) pairwise comparison matrices

S\'andor Boz\'oki, Vitaliy Tsyganok

arxiv:1701.04265 v3 · 2017-01-16 · 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{MK5MIAXCARXEEPAZ5GDF4TQ4G5}

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	2026-05-17T23:49:28.132473Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

62bac402e2046e423c19e9865e4e1c37543bf9599f7319556017ac8741675f6d

Aliases

arxiv: 1701.04265 · arxiv_version: 1701.04265v3 · doi: 10.48550/arxiv.1701.04265 · pith_short_12: MK5MIAXCARXE · pith_short_16: MK5MIAXCARXEEPAZ · pith_short_8: MK5MIAXC

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/MK5MIAXCARXEEPAZ5GDF4TQ4G5 \
  | 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: 62bac402e2046e423c19e9865e4e1c37543bf9599f7319556017ac8741675f6d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d9cedcc0d1cb0ddec7b87c8886e06dcab8adf152651b976717406cd1ccf4f717",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OC",
    "submitted_at": "2017-01-16T12:37:05Z",
    "title_canon_sha256": "c3732e31e827a6b797a98c1445b7331caa3518f195bb62e5c831908aeed25e5e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1701.04265",
    "kind": "arxiv",
    "version": 3
  }
}