Pith Number

pith:2E2B2KEY

pith:2025:2E2B2KEYOFAGBU4H2JRGM6Q36O

not attested not anchored not stored refs pending

Explicit solutions to Christoffel-Minkowski problems and Hessian equations under rotational symmetries

Fabian Mussnig, Jacopo Ulivelli

arxiv:2508.11600 v2 · 2025-08-15 · math.MG · math.AP · math.DG · math.FA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{2E2B2KEYOFAGBU4H2JRGM6Q36O}

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	2026-05-21T01:05:07.910258Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d1341d2898714060d387d262667a1bf38a7e082fe1786fc3dfe55c0743bafb02

Aliases

arxiv: 2508.11600 · arxiv_version: 2508.11600v2 · doi: 10.48550/arxiv.2508.11600 · pith_short_12: 2E2B2KEYOFAG · pith_short_16: 2E2B2KEYOFAGBU4H · pith_short_8: 2E2B2KEY

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/2E2B2KEYOFAGBU4H2JRGM6Q36O \
  | 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: d1341d2898714060d387d262667a1bf38a7e082fe1786fc3dfe55c0743bafb02

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5468d9c2dad91c11f6903e9e7efb3e2bfcadd696dba777a2f9b455477c27038f",
    "cross_cats_sorted": [
      "math.AP",
      "math.DG",
      "math.FA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.MG",
    "submitted_at": "2025-08-15T17:10:15Z",
    "title_canon_sha256": "57dcfb19cda7b52e702a5dc1c34a87c05fd5ab29f2ec936a31a3880835399eaf"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2508.11600",
    "kind": "arxiv",
    "version": 2
  }
}