Pith Number

pith:I7GIYYT3

pith:2024:I7GIYYT34F7PRHM2TMU3MNQ5IO

not attested not anchored not stored refs pending

Fractional Sobolev spaces on Riemannian manifolds

Enric Florit-Simon, Joaquim Serra, Michele Caselli

arxiv:2402.04076 v3 · 2024-01-17 · math.AP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{I7GIYYT34F7PRHM2TMU3MNQ5IO}

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.

Cited by

1 paper in Pith

Harmonic maps to the circle with higher dimensional singular set

Receipt and verification

First computed	2026-07-05T10:02:02.030183Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

47cc8c627be17ef89d9a9b29b6361d439a4be06d4ff1506cb17de996400c9388

Aliases

arxiv: 2402.04076 · arxiv_version: 2402.04076v3 · doi: 10.48550/arxiv.2402.04076 · pith_short_12: I7GIYYT34F7P · pith_short_16: I7GIYYT34F7PRHM2 · pith_short_8: I7GIYYT3

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/I7GIYYT34F7PRHM2TMU3MNQ5IO \
  | 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: 47cc8c627be17ef89d9a9b29b6361d439a4be06d4ff1506cb17de996400c9388

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "02d4e635c7138218f0154a362afe97b3a59bb0d2950eb74ecdfecaa1061732b0",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2024-01-17T09:19:28Z",
    "title_canon_sha256": "b4a154a01c3f6ede5fe18f4e412449dd736167d766236a5757b14978e5dca61f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2402.04076",
    "kind": "arxiv",
    "version": 3
  }
}