Pith Number

pith:NTTF4Z3A

pith:2026:NTTF4Z3AOBAR2A3TUBVZXQKO5M

not attested not anchored not stored refs pending

On zero-sum Ramsey numbers of cycles and wheels

Cheng Chi, Jialin He

R(C_qk, Z_q) equals qk + q - 1 exactly for odd q ≥ 3 and k ≥ 35q, with matching exact results for q=3 cycles and wheels W_3k.

arxiv:2605.14954 v1 · 2026-05-14 · math.CO

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\usepackage{pith}
\pithnumber{NTTF4Z3AOBAR2A3TUBVZXQKO5M}

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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

For every fixed odd q≥3 and every k≥35q, we obtain the exact value R(C_qk,Z_q)=qk+q-1. For q=3, R(C_3k,Z_3)=3k+2 for k≥2 and R(W_3k,Z_3)=3k+1 for k≥2.

C2weakest assumption

The upper bound for general q relies on Pikhurko's external result that R(C_2q,Z_q)≤35q²; if that bound is loose or inapplicable in the insertion step, the claimed exact value for large k would not hold.

C3one line summary

R(C_qk, Z_q) equals qk + q - 1 exactly for odd q ≥ 3 and k ≥ 35q, with matching exact results for q=3 cycles and wheels W_3k.

Receipt and verification

First computed	2026-05-17T23:38:55.356961Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6ce65e676070411d0373a06b9bc14eeb02233ced53f67f44413f14c52f7a423d

Aliases

arxiv: 2605.14954 · arxiv_version: 2605.14954v1 · doi: 10.48550/arxiv.2605.14954 · pith_short_12: NTTF4Z3AOBAR · pith_short_16: NTTF4Z3AOBAR2A3T · pith_short_8: NTTF4Z3A

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/NTTF4Z3AOBAR2A3TUBVZXQKO5M \
  | 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: 6ce65e676070411d0373a06b9bc14eeb02233ced53f67f44413f14c52f7a423d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "434b1584765c23e10b729ac46d391bda8adb39d32bf7ef49c4883b55be99946a",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2026-05-14T15:25:02Z",
    "title_canon_sha256": "c503f365e8e9fd6a1eb0080731ad670406367cbda2e1fe7c132d7e1698eb76d1"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.14954",
    "kind": "arxiv",
    "version": 1
  }
}