Pith Number

pith:NRAF6HS6

pith:2025:NRAF6HS64ZC3UTKGJ7DGW57QOV

not attested not anchored not stored refs pending

On the rigidity of manifolds with respect to Gagliardo-Nirenberg inequalities

Liang Cheng

arxiv:2507.05908 v2 · 2025-07-08 · 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{NRAF6HS64ZC3UTKGJ7DGW57QOV}

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	2026-07-05T11:43:33.349450Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6c405f1e5ee645ba4d464fc66b77f0754a22987dd3312d2c014e15f1504a2f33

Aliases

arxiv: 2507.05908 · arxiv_version: 2507.05908v2 · doi: 10.48550/arxiv.2507.05908 · pith_short_12: NRAF6HS64ZC3 · pith_short_16: NRAF6HS64ZC3UTKG · pith_short_8: NRAF6HS6

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/NRAF6HS64ZC3UTKGJ7DGW57QOV \
  | 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: 6c405f1e5ee645ba4d464fc66b77f0754a22987dd3312d2c014e15f1504a2f33

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4d2c4ff0f185d61583b59c46ee841ae0b114bdbb0cd2becda5ca95448e449c93",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2025-07-08T11:51:10Z",
    "title_canon_sha256": "a92742a8467fe8c65a7f436df89be05941d16ed70d3afd843617d8c572e33fff"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2507.05908",
    "kind": "arxiv",
    "version": 2
  }
}