Pith Number

pith:QPQBFWWY

pith:2026:QPQBFWWY4KCOA4YLEXRNMSXRHB

not attested not anchored not stored refs pending

Word-Representability of Shift Graphs

Ramesh Hariharasubramanian, Suchanda Roy

All shift graphs and their multi-shift generalizations are word-representable.

arxiv:2605.02268 v2 · 2026-05-04 · math.CO · cs.DM

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\usepackage{pith}
\pithnumber{QPQBFWWY4KCOA4YLEXRNMSXRHB}

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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

we prove that the entire class of shift graphs is word-representable. We also introduce a natural generalization of shift graphs in which adjacency is defined by more than one shift condition, and show that these generalized shift graphs are likewise word-representable.

C2weakest assumption

That a single word over the vertex alphabet can be arranged so the alternation condition holds simultaneously for every pair of adjacent and non-adjacent k-tuples under the given shift rules.

C3one line summary

Shift graphs G(n,k) and generalized shift graphs are word-representable.

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-25T02:01:21.586179Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

83e012dad8e284e0730b25e2d64af1384931542e3b19626f28724a2fb04c7e8b

Aliases

arxiv: 2605.02268 · arxiv_version: 2605.02268v2 · doi: 10.48550/arxiv.2605.02268 · pith_short_12: QPQBFWWY4KCO · pith_short_16: QPQBFWWY4KCOA4YL · pith_short_8: QPQBFWWY

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/QPQBFWWY4KCOA4YLEXRNMSXRHB \
  | 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: 83e012dad8e284e0730b25e2d64af1384931542e3b19626f28724a2fb04c7e8b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "474c185058f7f7df61d080c2b60d8a3b35e0fc5911297da511eb68a38cf36a7d",
    "cross_cats_sorted": [
      "cs.DM"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2026-05-04T06:21:59Z",
    "title_canon_sha256": "050d8603c5b2599d4e0bc2d229ee03958d484cccb7868e98fd4ee5329fed2d44"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.02268",
    "kind": "arxiv",
    "version": 2
  }
}