Pith Number

pith:7ULL5GKI

pith:2026:7ULL5GKITNZZHQUFSC3D76JHCL

not attested not anchored not stored refs pending

Cartan's and Gauss's equations and rigidity theorems for isometric embeddings in low Sobolev regularity

Isaac Newell, Luc Nguyen

arxiv:2607.02412 v1 · 2026-07-02 · math.AP · math.DG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{7ULL5GKITNZZHQUFSC3D76JHCL}

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	2026-07-03T01:17:58.446243Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

fd16be99489b7393c28590b63ff92712d6df76016d41e83e9bb1ef64b08573cc

Aliases

arxiv: 2607.02412 · arxiv_version: 2607.02412v1 · doi: 10.48550/arxiv.2607.02412 · pith_short_12: 7ULL5GKITNZZ · pith_short_16: 7ULL5GKITNZZHQUF · pith_short_8: 7ULL5GKI

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/7ULL5GKITNZZHQUFSC3D76JHCL \
  | 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: fd16be99489b7393c28590b63ff92712d6df76016d41e83e9bb1ef64b08573cc

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "19bf96357763202ae36805028003f33fa537d9d6be0b3c68a810e8c51094d3a5",
    "cross_cats_sorted": [
      "math.DG"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2026-07-02T16:44:12Z",
    "title_canon_sha256": "003d45893a3c1d2ceb5a839c94955332d97f179e7771e5d833e59a09f2d9ce14"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.02412",
    "kind": "arxiv",
    "version": 1
  }
}