Pith Number

pith:SYE6W3DB

pith:2026:SYE6W3DBCSOIJ5LJ66LD2XNQN3

not attested not anchored not stored refs pending

A sharp degree bound in the real Jacobian conjecture

B. Or\'efice-Okamoto, F. Braun, F. Fernandes, J. Gwo\'zdziewicz

Polynomial maps from the real plane to itself with one component of degree 6 and non-vanishing Jacobian determinant are injective.

arxiv:2605.12302 v2 · 2026-05-12 · math.AG · math.AC

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\usepackage{pith}
\pithnumber{SYE6W3DBCSOIJ5LJ66LD2XNQN3}

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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

if F=(p,q):R²→R² is a polynomial map such that the degree of p is 6 and whose Jacobian determinant is nowhere zero, then F is injective.

C2weakest assumption

The argument relies on a collection of earlier results for lower degrees and on standard facts about real polynomial rings and the topology of the plane; any gap in those cited results would propagate.

C3one line summary

Polynomial maps R²→R² with one component of degree 6 and nowhere-zero Jacobian are injective.

Receipt and verification

First computed	2026-05-26T01:03:33.668432Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9609eb6c61149c84f569f7963d5db06ee380d5ed9f3ab119b897f5b88411efe7

Aliases

arxiv: 2605.12302 · arxiv_version: 2605.12302v2 · doi: 10.48550/arxiv.2605.12302 · pith_short_12: SYE6W3DBCSOI · pith_short_16: SYE6W3DBCSOIJ5LJ · pith_short_8: SYE6W3DB

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/SYE6W3DBCSOIJ5LJ66LD2XNQN3 \
  | 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: 9609eb6c61149c84f569f7963d5db06ee380d5ed9f3ab119b897f5b88411efe7

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "358f64cac1326a1286a26df8d7262033ba549a54596b9ab0a0d23b5b8202b533",
    "cross_cats_sorted": [
      "math.AC"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2026-05-12T15:53:52Z",
    "title_canon_sha256": "8a06a13aecc739f639e2b350d357d43ce6fa8e5994d25834c3a19b43e44d750e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.12302",
    "kind": "arxiv",
    "version": 2
  }
}