Pith Number

pith:64YVKHKG

pith:2015:64YVKHKGIT3XA4XSHYNA7J5MIQ

not attested not anchored not stored refs pending

A critical point theorem on a closed ball and some applications to boundary value problems

Marek Galewski

arxiv:1503.06874 v1 · 2015-03-23 · 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{64YVKHKGIT3XA4XSHYNA7J5MIQ}

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	2026-05-18T02:20:29.885334Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f731551d4644f77072f23e1a0fa7ac442bf494c0a1313e65bed4c6e5b0679e0b

Aliases

arxiv: 1503.06874 · arxiv_version: 1503.06874v1 · doi: 10.48550/arxiv.1503.06874 · pith_short_12: 64YVKHKGIT3X · pith_short_16: 64YVKHKGIT3XA4XS · pith_short_8: 64YVKHKG

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/64YVKHKGIT3XA4XSHYNA7J5MIQ \
  | 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: f731551d4644f77072f23e1a0fa7ac442bf494c0a1313e65bed4c6e5b0679e0b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "80f214f60289a791bae054a07607789c220fbbe6fac7a37927942de9198aebb8",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2015-03-23T23:24:43Z",
    "title_canon_sha256": "6001c299d202f9e342965a505ee7b468f44b611fd8bc0abf06b21b89a9d46ef8"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1503.06874",
    "kind": "arxiv",
    "version": 1
  }
}