Pith Number

pith:7LUM665M

pith:2018:7LUM665MG3AP4EWCOVDTKRZHVJ

not attested not anchored not stored refs pending

Smooth approximations without critical points of continuous mappings between Banach spaces, and diffeomorphic extractions of sets

Daniel Azagra, Miguel Garc\'ia-Bravo, Tadeusz Dobrowolski

arxiv:1811.07587 v2 · 2018-11-19 · math.FA · 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{7LUM665MG3AP4EWCOVDTKRZHVJ}

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	2026-05-17T23:39:32.056546Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

fae8cf7bac36c0fe12c27547354727aa7c612d22f4b24ac005b0d2a27d43cad7

Aliases

arxiv: 1811.07587 · arxiv_version: 1811.07587v2 · doi: 10.48550/arxiv.1811.07587 · pith_short_12: 7LUM665MG3AP · pith_short_16: 7LUM665MG3AP4EWC · pith_short_8: 7LUM665M

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/7LUM665MG3AP4EWCOVDTKRZHVJ \
  | 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: fae8cf7bac36c0fe12c27547354727aa7c612d22f4b24ac005b0d2a27d43cad7

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6abc7ad9d1154ff72cfbfe65315429c6b73598c6f044ab1729cf8b1e306e20eb",
    "cross_cats_sorted": [
      "math.DG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2018-11-19T10:08:31Z",
    "title_canon_sha256": "9e14c205496c02190ac51415bf1612d717f80544bb57094b04a09251cf490428"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1811.07587",
    "kind": "arxiv",
    "version": 2
  }
}