Pith Number

pith:55BUN5S6

pith:2011:55BUN5S6IJKFOUXIXCL4GAQC4F

not attested not anchored not stored refs pending

Regularity at infinity of real mappings and a Morse-Sard theorem

L.R.G. Dias, M.A.S. Ruas, M. Tibar

arxiv:1103.5715 v1 · 2011-03-29 · math.AG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{55BUN5S6IJKFOUXIXCL4GAQC4F}

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	2026-05-18T02:58:01.063585Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ef4346f65e42545752e8b897c30202e15bdd32fe0a159521a99de3aede7a33c3

Aliases

arxiv: 1103.5715 · arxiv_version: 1103.5715v1 · doi: 10.48550/arxiv.1103.5715 · pith_short_12: 55BUN5S6IJKF · pith_short_16: 55BUN5S6IJKFOUXI · pith_short_8: 55BUN5S6

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/55BUN5S6IJKFOUXIXCL4GAQC4F \
  | 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: ef4346f65e42545752e8b897c30202e15bdd32fe0a159521a99de3aede7a33c3

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "00a597ea1402dcfcf902445d971f9f1695a3eed65d49a8123155c4f76347c4d8",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2011-03-29T17:36:05Z",
    "title_canon_sha256": "ff9984dae09e6653fac1e1c9dc9178e3914154d87426c11ac312778d532227ef"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1103.5715",
    "kind": "arxiv",
    "version": 1
  }
}