Pith Number

pith:JMBGZS33

pith:2024:JMBGZS33RCRNUBH2ZLTH45FV7Y

not attested not anchored not stored refs pending

Analytical obstructions to the weak approximation of Sobolev mappings into manifolds

Antoine Detaille, Jean Van Schaftingen

arxiv:2412.12889 v2 · 2024-12-17 · math.FA · 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{JMBGZS33RCRNUBH2ZLTH45FV7Y}

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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

Topological singular set of manifold-valued maps weakly approximable by smooth maps

Receipt and verification

First computed	2026-07-05T10:48:23.014570Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

4b026ccb7b88a2da04facae67e74b5fe276b5db0005ec34a01a796b046d192bb

Aliases

arxiv: 2412.12889 · arxiv_version: 2412.12889v2 · doi: 10.48550/arxiv.2412.12889 · pith_short_12: JMBGZS33RCRN · pith_short_16: JMBGZS33RCRNUBH2 · pith_short_8: JMBGZS33

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/JMBGZS33RCRNUBH2ZLTH45FV7Y \
  | 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: 4b026ccb7b88a2da04facae67e74b5fe276b5db0005ec34a01a796b046d192bb

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "84877b65d83d9a6496b94e70bd9054d8e68b559af2abc765731a15e700b11a18",
    "cross_cats_sorted": [
      "math.AP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2024-12-17T13:16:30Z",
    "title_canon_sha256": "ee76abfe5c293da1f18b25a66aff55131a1c6f5162d3241196c78f4fb61cafe9"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2412.12889",
    "kind": "arxiv",
    "version": 2
  }
}