Pith Number

pith:XUGT3B4K

pith:2017:XUGT3B4KINZU55RJAX5PDXTQLR

not attested not anchored not stored refs pending

Some remarks about The Morse-Sard theorem and approximate differentiability

Daniel Azagra, Miguel Garc\'ia-Bravo

arxiv:1705.05624 v1 · 2017-05-16 · math.FA · math.CA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{XUGT3B4KINZU55RJAX5PDXTQLR}

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	2026-05-18T00:44:20.606396Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

bd0d3d878a43734ef62905faf1de705c59fd2273e4212985c7a89591e64d5ac7

Aliases

arxiv: 1705.05624 · arxiv_version: 1705.05624v1 · doi: 10.48550/arxiv.1705.05624 · pith_short_12: XUGT3B4KINZU · pith_short_16: XUGT3B4KINZU55RJ · pith_short_8: XUGT3B4K

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/XUGT3B4KINZU55RJAX5PDXTQLR \
  | 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: bd0d3d878a43734ef62905faf1de705c59fd2273e4212985c7a89591e64d5ac7

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2b5f0481eee989fff885a4d7271782bd467c109e5c7e47c2935c13fcf93045e3",
    "cross_cats_sorted": [
      "math.CA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2017-05-16T10:03:27Z",
    "title_canon_sha256": "482217533230e07b2180e873956da7de047db2ba72f0525c7cee3a88addabc96"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1705.05624",
    "kind": "arxiv",
    "version": 1
  }
}