Pith Number

pith:WRLXL3AX

pith:2026:WRLXL3AX4HXICYXYN4UOC6BXIC

not attested not anchored not stored refs pending

An exact small-$n$ computation of the minimum 2-coloring discrepancy of $K_n^{(3)}$

Tong Niu

For n ≡ 1 or 3 mod 6 up to 21, the minimum 2-coloring discrepancy of Steiner triple systems equals min over x of |x(n-x)/2 - n(n-1)/12|.

arxiv:2605.00492 v2 · 2026-05-01 · math.CO

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\usepackage{pith}
\pithnumber{WRLXL3AX4HXICYXYN4UOC6BXIC}

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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

An exact value of δ₂(n) for each such n, matching the formula δ₂(n) = min_{x ∈ [0,n] ∩ Z} |x(n-x)/2 - n(n-1)/12| obtained by optimising the GGS Example 1.1 family.

C2weakest assumption

That simulated annealing finds the global minimum for n=13,15,19,21 and that the conjectural formula continues to hold for all larger n ≡1,3 mod 6.

C3one line summary

Exact values of δ₂(n) for n=7,9,13,15,19,21 match the min over x of |x(n-x)/2 - n(n-1)/12|, with a conjecture that this holds for all n ≡1,3 mod 6.

Receipt and verification

First computed	2026-06-19T16:10:55.490221Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b45775ec17e1ee8162f86f28e17837409b03db67bcda456626af9a4d142b4630

Aliases

arxiv: 2605.00492 · arxiv_version: 2605.00492v2 · doi: 10.48550/arxiv.2605.00492 · pith_short_12: WRLXL3AX4HXI · pith_short_16: WRLXL3AX4HXICYXY · pith_short_8: WRLXL3AX

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/WRLXL3AX4HXICYXYN4UOC6BXIC \
  | 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: b45775ec17e1ee8162f86f28e17837409b03db67bcda456626af9a4d142b4630

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d9705e14f49e5a5c11fb435b73a09612e724f72cc36767d09eac5b424caf71bf",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2026-05-01T08:02:38Z",
    "title_canon_sha256": "d2d8276a6c8bcaf648628abf6d558739c50a55789afc2f0e126c068d363c7045"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.00492",
    "kind": "arxiv",
    "version": 2
  }
}