Pith Number

pith:NNX6FRHN

pith:2025:NNX6FRHN22VM2SLPHAZNTZ5GJR

not attested not anchored not stored refs pending

Well quasi-order and atomicity for combinatorial structures under consecutive orders

Nik Ru\v{s}kuc, Victoria Ironmonger

A general framework decides well quasi-order and atomicity for avoidance sets of combinatorial structures under consecutive orders.

arxiv:2510.01852 v5 · 2025-10-02 · math.CO

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\usepackage{pith}
\pithnumber{NNX6FRHN22VM2SLPHAZNTZ5GJR}

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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

✓ 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

We will establish a general framework, which enables us to answer these problems for a wide class of combinatorial structures, including graphs, digraphs and collections of relations.

C2weakest assumption

That the consecutive embedding order on the structures permits the extension of recent approaches into a single general framework that covers the stated wide class without additional restrictions.

C3one line summary

Establishes a general framework to answer decidability questions on well quasi-order and atomicity for avoidance sets in posets of combinatorial structures under consecutive orders, covering graphs, digraphs and relations.

Receipt and verification

First computed	2026-06-01T01:02:22.242186Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6b6fe2c4edd6aacd496f3832d9e7a64c69b17f3d664f00cbe44880a7b8079ceb

Aliases

arxiv: 2510.01852 · arxiv_version: 2510.01852v5 · doi: 10.48550/arxiv.2510.01852 · pith_short_12: NNX6FRHN22VM · pith_short_16: NNX6FRHN22VM2SLP · pith_short_8: NNX6FRHN

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/NNX6FRHN22VM2SLPHAZNTZ5GJR \
  | 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: 6b6fe2c4edd6aacd496f3832d9e7a64c69b17f3d664f00cbe44880a7b8079ceb

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "463b2bd0eb91c966c6ae5a0464cc40b715f056c6963b9a27ee546c3ac7e5a759",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2025-10-02T09:51:54Z",
    "title_canon_sha256": "3beb66278feb38bd7c834eeefd0d25e8082e49fd3dd8adc3c97c2f31339b4426"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2510.01852",
    "kind": "arxiv",
    "version": 5
  }
}