Pith Number

pith:ZXFDGYRK

pith:2026:ZXFDGYRKDYN4KU2VEZHWPURUR7

not attested not anchored not stored refs pending

The Non-Orientable Topology of Condorcet's Paradox

Mikhail Prokopenko, Ori Livson, Siddharth Pritam

Condorcet's Paradox corresponds to the non-orientability of a Klein bottle or real projective plane.

arxiv:2601.07283 v4 · 2026-01-12 · math.AT · cs.GT · econ.TH

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\usepackage{pith}
\pithnumber{ZXFDGYRKDYN4KU2VEZHWPURUR7}

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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.

Claims

C1strongest claim

the contradiction underlying Condorcet's Paradox topologically corresponds to the non-orientability of a surface homeomorphic to either the Klein Bottle or Real Projective Plane, depending on how preference cycles are represented

C2weakest assumption

that the chosen topological representation of preference cycles (generalizing Baryshnikov's model for strict ordinal preferences on three alternatives) faithfully captures the logical contradiction without introducing extraneous structure

C3one line summary

Condorcet's paradox corresponds to non-orientability of a surface homeomorphic to the Klein bottle or real projective plane in a generalized topological model of strict ordinal preferences.

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-06-19T16:10:34.254053Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

cdca33622a1e1bc55355264f67d2348fc21080c68c89d23bf34e9fcb3f697867

Aliases

arxiv: 2601.07283 · arxiv_version: 2601.07283v4 · doi: 10.48550/arxiv.2601.07283 · pith_short_12: ZXFDGYRKDYN4 · pith_short_16: ZXFDGYRKDYN4KU2V · pith_short_8: ZXFDGYRK

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/ZXFDGYRKDYN4KU2VEZHWPURUR7 \
  | 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: cdca33622a1e1bc55355264f67d2348fc21080c68c89d23bf34e9fcb3f697867

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "787f1a2f54867183e728b774b0b05f883290a8da40cda76c94087dcc65651f23",
    "cross_cats_sorted": [
      "cs.GT",
      "econ.TH"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AT",
    "submitted_at": "2026-01-12T07:38:25Z",
    "title_canon_sha256": "d8d2426ded51afb206f997963fbf1470a580c455313b5cc97ac7f2f0422392ab"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2601.07283",
    "kind": "arxiv",
    "version": 4
  }
}