Pith Number

pith:ULZB2I7G

pith:2011:ULZB2I7GBEGMDUVTPLDHHUTCEJ

not attested not anchored not stored refs pending

Minimal time functions and the smallest intersecting ball problem generated by unbounded dynamics

Cristina Villalobos, Nguyen Mau Nam, Nguyen Thai An

arxiv:1112.5688 v2 · 2011-12-24 · math.OC

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{ULZB2I7GBEGMDUVTPLDHHUTCEJ}

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	2026-05-18T04:05:26.568747Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a2f21d23e6090cc1d2b37ac673d262225e0e84421188ff1cc8baa7e4b241b9f6

Aliases

arxiv: 1112.5688 · arxiv_version: 1112.5688v2 · doi: 10.48550/arxiv.1112.5688 · pith_short_12: ULZB2I7GBEGM · pith_short_16: ULZB2I7GBEGMDUVT · pith_short_8: ULZB2I7G

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/ULZB2I7GBEGMDUVTPLDHHUTCEJ \
  | 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: a2f21d23e6090cc1d2b37ac673d262225e0e84421188ff1cc8baa7e4b241b9f6

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0071261f8f67bc7458c85b6e31b05d0fdd28b27d579da092736579b443e334a1",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OC",
    "submitted_at": "2011-12-24T02:57:48Z",
    "title_canon_sha256": "bcfa3f7c6bd3970e2b36b1c9346ccfe5f42bacac6e5871e02f33bb173323ce15"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1112.5688",
    "kind": "arxiv",
    "version": 2
  }
}