Pith Number

pith:G5645FQH

pith:2018:G5645FQHSAOLATHSSJHJBHHS3E

not attested not anchored not stored refs pending

A simple counterexample to the Monge ansatz in multi-marginal optimal transport, convex geometry of the set of Kantorovich plans, and the Frenkel-Kontorova model

Gero Friesecke

arxiv:1808.04318 v1 · 2018-08-13 · math.AP · math-ph · math.MP · 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{G5645FQHSAOLATHSSJHJBHHS3E}

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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	2026-05-18T00:08:16.695383Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

377dce9607901cb04cf2924e909cf2d90700a23457a7b7e69cfe51dae26c3649

Aliases

arxiv: 1808.04318 · arxiv_version: 1808.04318v1 · doi: 10.48550/arxiv.1808.04318 · pith_short_12: G5645FQHSAOL · pith_short_16: G5645FQHSAOLATHS · pith_short_8: G5645FQH

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/G5645FQHSAOLATHSSJHJBHHS3E \
  | 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: 377dce9607901cb04cf2924e909cf2d90700a23457a7b7e69cfe51dae26c3649

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ad0b34e0ec5786637819f1493fbf1eb8ecf0ac3a936a0d94ea63b40bba148b8b",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP",
      "math.OC"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2018-08-13T16:22:25Z",
    "title_canon_sha256": "6d73a17c953a8a0af9301f650ed9ca0dbc985b5617ed5e3303372ed24e4f7cf6"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1808.04318",
    "kind": "arxiv",
    "version": 1
  }
}