Pith Number

pith:WW3CVALF

pith:2015:WW3CVALFA7JROHVJEXI3W5CA5O

not attested not anchored not stored refs pending

Gagliardo-Nirenberg Inequalities for Differential Forms in Heisenberg Groups

Annalisa Baldi, Bruno Franchi, Pierre Pansu

arxiv:1506.05904 v1 · 2015-06-19 · 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{WW3CVALFA7JROHVJEXI3W5CA5O}

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	2026-05-18T01:42:46.932106Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b5b62a816507d3171ea925d1bb7440eba64fc85271456354e36b27e80428d20a

Aliases

arxiv: 1506.05904 · arxiv_version: 1506.05904v1 · doi: 10.48550/arxiv.1506.05904 · pith_short_12: WW3CVALFA7JR · pith_short_16: WW3CVALFA7JROHVJ · pith_short_8: WW3CVALF

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/WW3CVALFA7JROHVJEXI3W5CA5O \
  | 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: b5b62a816507d3171ea925d1bb7440eba64fc85271456354e36b27e80428d20a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9edf72a4b3d6c2fea98ceab8bb984edc8a43da5150c884663b01c294d6032cb8",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2015-06-19T08:24:31Z",
    "title_canon_sha256": "05cbb6ab79380538f7ee22f651db28779024de8c1aba59e0ecad818834ac6f52"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1506.05904",
    "kind": "arxiv",
    "version": 1
  }
}