Pith Number

pith:2LK6SAIP

pith:2026:2LK6SAIPSPMVG754WABLG7IKTW

not attested not anchored not stored refs pending

Existence and Counting Bounds for High-Memory Spatially-Coupled Codes via the Combinatorial Nullstellensatz

Lei Huang

Applies Combinatorial Nullstellensatz to derive sufficient memory conditions for SC-LDPC protographs to destroy all 4-cycles and all 4- and 6-cycles, plus lower bounds on the number of such feasible edge-spreading assignments.

arxiv:2605.18323 v1 · 2026-05-18 · cs.IT · math.IT

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\usepackage{pith}
\pithnumber{2LK6SAIPSPMVG754WABLG7IKTW}

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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

For fully connected (γ,κ) base graphs, the resulting bounds explicitly characterize the memory required to destroy all 4-cycles as well as all 4- and 6-cycles, and for fixed γ, they are asymptotically tight up to a constant factor compared with known lower bounds.

C2weakest assumption

Cycle-activation conditions for the harmful structures can be encoded as polynomial vanishing constraints over finite grids in a way that permits direct application of the Combinatorial Nullstellensatz to obtain the stated memory thresholds.

C3one line summary

Receipt and verification

First computed	2026-05-20T00:05:55.174913Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d2d5e9010f93d9537fbcb002b37d0a9d930e1283ba6d1983b092793d08b5a3c1

Aliases

arxiv: 2605.18323 · arxiv_version: 2605.18323v1 · doi: 10.48550/arxiv.2605.18323 · pith_short_12: 2LK6SAIPSPMV · pith_short_16: 2LK6SAIPSPMVG754 · pith_short_8: 2LK6SAIP

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/2LK6SAIPSPMVG754WABLG7IKTW \
  | 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: d2d5e9010f93d9537fbcb002b37d0a9d930e1283ba6d1983b092793d08b5a3c1

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "13977cdda210f766c7b2ef1bfeac4b4390e05a23cc5a4b5a3142659264b06256",
    "cross_cats_sorted": [
      "math.IT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.IT",
    "submitted_at": "2026-05-18T12:41:53Z",
    "title_canon_sha256": "98a99172106e2ef9ae0b4f411a481ac8ba0e3ce491a34283fea3af7c47c7545a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.18323",
    "kind": "arxiv",
    "version": 1
  }
}