Pith Number

pith:HEOZJQRY

pith:2025:HEOZJQRYHZKP2VDTVPVO6TORW2

not attested not anchored not stored refs pending

Nowhere-zero flow reconfiguration

Aur\'elie Lagoutte, Kevin Hendrey, Louis Esperet, Margaux Marseloo, Raphael Steiner, Sergey Norin

All nowhere-zero Z_2^8-flows on every 2-edge-connected graph are connected by sequences differing on single cycles.

arxiv:2512.17342 v4 · 2025-12-19 · math.CO · 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{HEOZJQRYHZKP2VDTVPVO6TORW2}

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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

All nowhere-zero Z_2^8-flows of every 2-edge-connected graph are connected and for every sufficiently large abelian group A, all nowhere-zero A-flows of every 2-edge-connected graph are connected.

C2weakest assumption

The graph is 2-edge-connected, which is required for the existence and reconfiguration properties of nowhere-zero flows to hold in the stated forms.

C3one line summary

Nowhere-zero flows on 2-edge-connected graphs can be reconfigured via successive cycle changes for Z_2^8-flows and sufficiently large groups, but the 5-flow reconfiguration conjecture is false, with group structure mattering unlike existence.

Cited by

2 papers in Pith

Reconfiguration of Nowhere-zero Flows

A QUBO Formulation for Nowhere-Zero $k$-Flows

Receipt and verification

First computed	2026-07-07T01:16:02.434298Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

391d94c2383e54fd5473abeaef4dd1b6bb1313db1fd74c59340051e8c910eec8

Aliases

arxiv: 2512.17342 · arxiv_version: 2512.17342v4 · doi: 10.48550/arxiv.2512.17342 · pith_short_12: HEOZJQRYHZKP · pith_short_16: HEOZJQRYHZKP2VDT · pith_short_8: HEOZJQRY

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/HEOZJQRYHZKP2VDTVPVO6TORW2 \
  | 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: 391d94c2383e54fd5473abeaef4dd1b6bb1313db1fd74c59340051e8c910eec8

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "fe1836a759056c7858926812fd5ba2677908d642fe6aad21c9e2cc17de08aa5f",
    "cross_cats_sorted": [
      "cs.DM"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2025-12-19T08:34:36Z",
    "title_canon_sha256": "be5e0895ca3721c0c10d7ce054bea574b3d141a0593ac659ad62d61dec272e42"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2512.17342",
    "kind": "arxiv",
    "version": 4
  }
}