Pith Number

pith:PNVFPA7F

pith:2018:PNVFPA7FXHUYGBCTGN3HRMKOWQ

not attested not anchored not stored refs pending

Differential structure associated to axiomatic Sobolev spaces

Enrico Pasqualetto, Nicola Gigli

arxiv:1807.05417 v1 · 2018-07-14 · 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{PNVFPA7FXHUYGBCTGN3HRMKOWQ}

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	2026-05-18T00:10:43.608085Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7b6a5783e5b9e9830453337678b14eb4293c9d22ca789cb17951b9612e2944b3

Aliases

arxiv: 1807.05417 · arxiv_version: 1807.05417v1 · doi: 10.48550/arxiv.1807.05417 · pith_short_12: PNVFPA7FXHUY · pith_short_16: PNVFPA7FXHUYGBCT · pith_short_8: PNVFPA7F

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/PNVFPA7FXHUYGBCTGN3HRMKOWQ \
  | 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: 7b6a5783e5b9e9830453337678b14eb4293c9d22ca789cb17951b9612e2944b3

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "76f12b3a1d4bae91e3695c215ff0a0c4b65e0a70aca7eff9300e510402ebf2b0",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2018-07-14T16:19:49Z",
    "title_canon_sha256": "a6abcf10988a4153a231db323228a7ed48bf24d5b022574c951fdce74a11dac4"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1807.05417",
    "kind": "arxiv",
    "version": 1
  }
}