Pith Number

pith:D37GFZX7

pith:2019:D37GFZX7R2NYI6DLPYB7QCEBLR

not attested not anchored not stored refs pending

Smallness of the set of critical values of distance functions in two-dimensional Euclidean and Riemannian spaces

Jan Rataj, Ludek Zajicek

arxiv:1903.09492 v1 · 2019-03-22 · math.MG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{D37GFZX7R2NYI6DLPYB7QCEBLR}

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	2026-07-05T00:59:21.494117Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1efe62e6ff8e9b84786b7e03f808815c7bc19bc4086edc21cfd272e4f0f8cf20

Aliases

arxiv: 1903.09492 · arxiv_version: 1903.09492v1 · doi: 10.48550/arxiv.1903.09492 · pith_short_12: D37GFZX7R2NY · pith_short_16: D37GFZX7R2NYI6DL · pith_short_8: D37GFZX7

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/D37GFZX7R2NYI6DLPYB7QCEBLR \
  | 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: 1efe62e6ff8e9b84786b7e03f808815c7bc19bc4086edc21cfd272e4f0f8cf20

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5015d8d23180e9f654708512f4d79415f6c92bc2e7df3c2b66f8ee4ef05d5728",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.MG",
    "submitted_at": "2019-03-22T13:22:14Z",
    "title_canon_sha256": "5d5fd4f2f7b586167e8d0724f4023c77a54b12ebfdd40205a2b57497a8dedb66"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1903.09492",
    "kind": "arxiv",
    "version": 1
  }
}