Pith Number

pith:V7F34HJL

pith:2016:V7F34HJLF6GMCYZ2VGTWRDX7YO

not attested not anchored not stored refs pending

LAST but not Least: Online Spanners for Buy-at-Bulk

Anupam Gupta, Kunal Talwar, R. Ravi, Seeun William Umboh

arxiv:1611.00052 v1 · 2016-10-31 · cs.DS

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{V7F34HJLF6GMCYZ2VGTWRDX7YO}

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	2026-05-18T01:00:41.511482Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

afcbbe1d2b2f8cc1633aa9a7688effc3916bb5cec33b5aa8e08a44ae383786a3

Aliases

arxiv: 1611.00052 · arxiv_version: 1611.00052v1 · doi: 10.48550/arxiv.1611.00052 · pith_short_12: V7F34HJLF6GM · pith_short_16: V7F34HJLF6GMCYZ2 · pith_short_8: V7F34HJL

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/V7F34HJLF6GMCYZ2VGTWRDX7YO \
  | 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: afcbbe1d2b2f8cc1633aa9a7688effc3916bb5cec33b5aa8e08a44ae383786a3

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "50a85b975fdb66d1aa34dc6bf22f09048dc30b3aae076c97f40a33cd32acee67",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.DS",
    "submitted_at": "2016-10-31T21:34:05Z",
    "title_canon_sha256": "2089ae1386b088351b435a2611cd0cc865be6b3548c95fdfd01175c000d4c763"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1611.00052",
    "kind": "arxiv",
    "version": 1
  }
}