Pith Number

pith:WGL6XY2H

pith:2025:WGL6XY2H7VT2UPIUR2YNGRUMSO

not attested not anchored not stored refs pending

Embeddings and intersections of adelic groups

Dmitry Badulin

On three-dimensional regular projective varieties over countable fields, the intersection A_I(X,F) ∩ A_J(X,F) equals A_{I∩J}(X,F) for locally free sheaves F.

arxiv:2510.22408 v3 · 2025-10-25 · math.AG · math.AC

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\usepackage{pith}
\pithnumber{WGL6XY2H7VT2UPIUR2YNGRUMSO}

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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

On a three-dimensional regular projective variety over a countable field the intersection A_I(X,F) ∩ A_J(X,F) equals A_{I∩J}(X,F) for any I,J ⊂ {0,1,2,3} and any locally free sheaf F on X.

C2weakest assumption

The underlying scheme must be normal excellent of special type, or Cohen-Macaulay projective, or three-dimensional regular projective over a countable field (as stated in the respective theorems).

C3one line summary

Proves embeddings and intersection equalities for adelic groups on excellent and projective schemes, plus a limit result for global sections of locally free sheaves.

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-07-09T00:19:11.476717Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b197ebe347fd67aa3d148eb0d3468c938e2585f98bee638d75718ecb134ed156

Aliases

arxiv: 2510.22408 · arxiv_version: 2510.22408v3 · doi: 10.48550/arxiv.2510.22408 · pith_short_12: WGL6XY2H7VT2 · pith_short_16: WGL6XY2H7VT2UPIU · pith_short_8: WGL6XY2H

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/WGL6XY2H7VT2UPIUR2YNGRUMSO \
  | 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: b197ebe347fd67aa3d148eb0d3468c938e2585f98bee638d75718ecb134ed156

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "71ad210e5578fd65b556a1ea9e0fa1240052bc005e74d4a8e8d60cc91944726e",
    "cross_cats_sorted": [
      "math.AC"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2025-10-25T19:08:22Z",
    "title_canon_sha256": "b26d2dde21e16d04693a5144bb17f9fa987cf7a86fb24b5a4bce23c1c5a7e32c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2510.22408",
    "kind": "arxiv",
    "version": 3
  }
}