Pith Number

pith:TIXWZLA2

pith:2026:TIXWZLA2CA7D5HMSTMCATKY3MO

not attested not anchored not stored refs resolved

Explicitly combing hedgehogs over fields of Stufe 4

Peter M\"uller

Explicit formulas produce a matrix in SL_3 over the unit sphere ring from four squares summing to minus one.

arxiv:2605.15452 v1 · 2026-05-14 · math.NT · math.AG

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\pithnumber{TIXWZLA2CA7D5HMSTMCATKY3MO}

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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

We construct an explicit example in terms of a,b,c,d of a matrix in SL_3(K[x,y,z]) with first row (x,y,z) whenever a² + b² + c² + d² = -1 in K.

C2weakest assumption

The algebraic identities that define the matrix entries from a,b,c,d remain valid inside the quotient ring K[x,y,z]/(x²+y²+z²-1) and produce determinant 1; this is invoked when the explicit formulas are substituted and simplified.

C3one line summary

Explicit matrix in SL_3(K[x,y,z]) with first row (x,y,z) for any field K of Stufe at most 4, expressed in terms of a,b,c,d satisfying a²+b²+c²+d²=-1.

References

4 extracted · 4 resolved · 0 Pith anchors

[1] Combing a hedgehog over a field 2025 · doi:10.2140/ant

[2] msolve: A Library for Solv- ing Polynomial Systems 2021 · doi:10.1145/3452143.3465545

[3] Müller.SageMath verification script.https://ypfmde.github.io/ verify_combing.html 2026

[4] https://www.sagemath.org 2022

Receipt and verification

First computed	2026-05-20T00:00:59.347040Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9a2f6cac1a103e3e9d929b0409ab1b6390eab98b7fd2a277e555d0606473fa63

Aliases

arxiv: 2605.15452 · arxiv_version: 2605.15452v1 · doi: 10.48550/arxiv.2605.15452 · pith_short_12: TIXWZLA2CA7D · pith_short_16: TIXWZLA2CA7D5HMS · pith_short_8: TIXWZLA2

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/TIXWZLA2CA7D5HMSTMCATKY3MO \
  | 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: 9a2f6cac1a103e3e9d929b0409ab1b6390eab98b7fd2a277e555d0606473fa63

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f7c504951f1de88b8024a0e201ce3d5e0396317ab354865831294a83aa233a15",
    "cross_cats_sorted": [
      "math.AG"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2026-05-14T22:29:02Z",
    "title_canon_sha256": "2b452565bd7fd92a06a11bb264ad7fa58892fc738d408e3d31bdfc1731dfe24f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.15452",
    "kind": "arxiv",
    "version": 1
  }
}