Pith Number

pith:2VAKVXCY

pith:2026:2VAKVXCYVV4RWT65NAEFDM3KQB

not attested not anchored not stored refs resolved

Relative accessibility for graphs

Joseph Paul MacManus

Relative accessibility for graphs is characterized by a subring of the Boolean ring and matches the algebraic definition for groups.

arxiv:2605.12629 v1 · 2026-05-12 · math.CO · math.GR

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\usepackage{pith}
\pithnumber{2VAKVXCYVV4RWT65NAEFDM3KQB}

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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

In the case of locally finite, quasi-transitive graphs, we characterise relative accessibility in terms of a certain subring of the Boolean ring of the graph, and apply this to show that our definition agrees with the usual algebraic notion of relative accessibility in finitely generated groups.

C2weakest assumption

The graphs are locally finite and quasi-transitive, and any quasi-isometry under consideration coarsely preserves the left cosets of the peripheral subgroups.

C3one line summary

Relative accessibility in graphs is defined relative to peripheral systems, characterized via Boolean ring subrings for quasi-transitive graphs, and shown to match the group-theoretic version while being quasi-isometry invariant when cosets are preserved.

References

31 extracted · 31 resolved · 2 Pith anchors

[1] arXiv preprint arXiv:0708.0920 , year= · arXiv:0708.0920

[2] Quasi-actions on trees and property ( 2006

[3] The electronic journal of combinatorics , volume=

[4] International Journal of Algebra and Computation , volume= 2014

[5] Metric spaces of non-positive curvature , author=. 2013 , publisher= 2013

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-18T03:10:00.219910Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d540aadc58ad791b4fdd680851b36a806c83850020fe8649b436fd96415452ce

Aliases

arxiv: 2605.12629 · arxiv_version: 2605.12629v1 · doi: 10.48550/arxiv.2605.12629 · pith_short_12: 2VAKVXCYVV4R · pith_short_16: 2VAKVXCYVV4RWT65 · pith_short_8: 2VAKVXCY

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/2VAKVXCYVV4RWT65NAEFDM3KQB \
  | 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: d540aadc58ad791b4fdd680851b36a806c83850020fe8649b436fd96415452ce

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3967b3c1f420aa8e2859db1ed4a8193c1536f5f2ab0739d6b58b60f032045fb2",
    "cross_cats_sorted": [
      "math.GR"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2026-05-12T18:12:33Z",
    "title_canon_sha256": "c0b231659902ff4865a6671e26fcd46045c7af5c1dbcb0785dde04519c4bbb03"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.12629",
    "kind": "arxiv",
    "version": 1
  }
}