Pith Number

pith:MMUHTO5U

pith:2010:MMUHTO5ULEWNL4AQ7VQERMAX6W

not attested not anchored not stored refs pending

Metric Extension Operators, Vertex Sparsifiers and Lipschitz Extendability

Konstantin Makarychev, Yury Makarychev

arxiv:1006.4607 v2 · 2010-06-23 · 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{MMUHTO5ULEWNL4AQ7VQERMAX6W}

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	2026-05-18T04:33:49.671062Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

632879bbb4592cd5f010fd6048b017f58854c9ba98daa6887bd281afcaf3ba9c

Aliases

arxiv: 1006.4607 · arxiv_version: 1006.4607v2 · doi: 10.48550/arxiv.1006.4607 · pith_short_12: MMUHTO5ULEWN · pith_short_16: MMUHTO5ULEWNL4AQ · pith_short_8: MMUHTO5U

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/MMUHTO5ULEWNL4AQ7VQERMAX6W \
  | 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: 632879bbb4592cd5f010fd6048b017f58854c9ba98daa6887bd281afcaf3ba9c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ce39eb89bff6550820fee74c8651d56ea0d40f13fe42ba320a73f28ed86761d3",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.DS",
    "submitted_at": "2010-06-23T18:43:33Z",
    "title_canon_sha256": "742eeab944ace74338f00e470be7a73712af3e2ec3c0a145aa82af97057d4b72"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1006.4607",
    "kind": "arxiv",
    "version": 2
  }
}