Pith Number

pith:SC7OWC3M

pith:2025:SC7OWC3MX433OR2EZXRODMAANI

not attested not anchored not stored refs pending

North-East Lattice Paths Avoiding $k$ Collinear Points via Satisfiability

Aaron Barnoff, Curtis Bright

Satisfiability solvers classify all north-east lattice paths avoiding up to six collinear points and find a 327-step example for seven.

arxiv:2511.23226 v2 · 2025-11-28 · math.CO · cs.DM · cs.LO

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\usepackage{pith}
\pithnumber{SC7OWC3MX433OR2EZXRODMAANI}

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Record completeness

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2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

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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

We also find a north-east lattice path avoiding k = 7 collinear points with 327 steps, improving on the previous best length of 260 steps found by Shallit.

C2weakest assumption

The SAT encoding correctly captures the collinearity-avoidance condition and the solver's search is exhaustive up to isomorphism for k≤6 and finds a valid 327-step example for k=7.

C3one line summary

SAT solvers enumerate all north-east lattice paths avoiding k collinear points for k≤6 and produce a 327-step path for k=7, improving the prior record of 260 steps.

Receipt and verification

First computed	2026-05-20T00:02:59.585505Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

90beeb0b6cbf37b74744cde2e1b0006a2894edfcda4a8b222e2e4bbe672635a5

Aliases

arxiv: 2511.23226 · arxiv_version: 2511.23226v2 · doi: 10.48550/arxiv.2511.23226 · pith_short_12: SC7OWC3MX433 · pith_short_16: SC7OWC3MX433OR2E · pith_short_8: SC7OWC3M

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/SC7OWC3MX433OR2EZXRODMAANI \
  | 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: 90beeb0b6cbf37b74744cde2e1b0006a2894edfcda4a8b222e2e4bbe672635a5

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4b45024312406ceb27607ba42d3457058853b5e83107d6b51d58902dd6201896",
    "cross_cats_sorted": [
      "cs.DM",
      "cs.LO"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2025-11-28T14:34:26Z",
    "title_canon_sha256": "80483a16a9d4dff14d7fce707ada7d433e486e1c256d15ec5ab1f92a663c772d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2511.23226",
    "kind": "arxiv",
    "version": 2
  }
}