Pith Number

pith:5UDTPJWV

pith:2026:5UDTPJWVAYGJ26RBFR6GGANGRI

not attested not anchored not stored refs resolved

A Classical Analysis Counterpart of Viterbo's Symplectic Geometry Proof of ABP in the Plane

Daniel Maienshein, Juan J. Manfredi

A classical analysis proof gives the Alexandroff-Bakelman-Pucci inequality in the plane for compactly supported C² functions without using convexity or contact sets.

arxiv:2605.12712 v1 · 2026-05-12 · math.AP

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{5UDTPJWVAYGJ26RBFR6GGANGRI}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more · Embed verified badge

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

We first provide a classical analysis proof of a version of the Alexandroff-Bakelman-Pucci inequality (ABP) for compactly supported C² functions in dimension 2, inspired by the symplectic geometry proof method of Viterbo, which avoids convexity or contact sets.

C2weakest assumption

The translation from the symplectic geometry argument to classical analysis steps preserves the key estimates without hidden use of convexity or contact-set properties, which is asserted but not verified in the abstract alone.

C3one line summary

A classical analysis proof of the ABP inequality in the plane is constructed for compactly supported C² functions and then extended to the standard form with a boundary term.

References

7 extracted · 7 resolved · 0 Pith anchors

[1] Journal of the American Mathematical Society , volume=

[2] Mathematische Annalen , volume=

[3] Foundations of differentiable manifolds and Lie groups , author=. 1983 , publisher= 1983

[4] On the alexandroff-bakelman-pucci estimate and the reversed h 1995

[5] Geometric measure theory , author=. 1969 , publisher= 1969

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-18T03:09:49.525773Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ed0737a6d5060c9d7a212c7c6301a68a21eadbddf8e3f5561c913a0e33e7b6ab

Aliases

arxiv: 2605.12712 · arxiv_version: 2605.12712v1 · doi: 10.48550/arxiv.2605.12712 · pith_short_12: 5UDTPJWVAYGJ · pith_short_16: 5UDTPJWVAYGJ26RB · pith_short_8: 5UDTPJWV

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/5UDTPJWVAYGJ26RBFR6GGANGRI \
  | 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: ed0737a6d5060c9d7a212c7c6301a68a21eadbddf8e3f5561c913a0e33e7b6ab

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "00fd7f5f97d79d183fd199888011446c3afe1ed7749a0a76b204b3b8c0111844",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2026-05-12T20:21:20Z",
    "title_canon_sha256": "400a68f33786d5ca2c0f1e1276775a38f1a9ee101a4559c088f7892d9a170a87"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.12712",
    "kind": "arxiv",
    "version": 1
  }
}