Pith Number

pith:3DN5SZXR

pith:2025:3DN5SZXRYDVM2DUUCOADNG4Z4J

not attested not anchored not stored refs pending

A self-contained proof of the Alt-Caffarelli-Friedman monotonicity formula

Emanuele Salato

arxiv:2506.13473 v2 · 2025-06-16 · 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{3DN5SZXRYDVM2DUUCOADNG4Z4J}

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.

Receipt and verification

First computed	2026-05-22T01:03:14.787658Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d8dbd966f1c0eacd0e941380369b99e2437196431f6d7e489c86e9fdcdbe40a5

Aliases

arxiv: 2506.13473 · arxiv_version: 2506.13473v2 · doi: 10.48550/arxiv.2506.13473 · pith_short_12: 3DN5SZXRYDVM · pith_short_16: 3DN5SZXRYDVM2DUU · pith_short_8: 3DN5SZXR

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/3DN5SZXRYDVM2DUUCOADNG4Z4J \
  | 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: d8dbd966f1c0eacd0e941380369b99e2437196431f6d7e489c86e9fdcdbe40a5

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ab778d819054c490fd7323cb526b4b200da431ce08971bb3876bb63882ff3b24",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2025-06-16T13:31:32Z",
    "title_canon_sha256": "b94c633221728301e5594b78222122dd56f7c2cfefa3fb1f22707975b554f0c9"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2506.13473",
    "kind": "arxiv",
    "version": 2
  }
}