Pith Number

pith:HMDAHOAQ

pith:2006:HMDAHOAQCYQK6JM2L4YEPOE7E5

not attested not anchored not stored refs pending

Embedding Metrics into Ultrametrics and Graphs into Spanning Trees with Constant Average Distortion

Ittai Abraham, Ofer Neiman, Yair Bartal

arxiv:cs/0610003 v2 · 2006-10-01 · cs.DM

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{HMDAHOAQCYQK6JM2L4YEPOE7E5}

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	2026-05-18T01:06:48.923454Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3b0603b8101620af259a5f3047b89f274ac3b3bbee9351291e535f7d0db5cf96

Aliases

arxiv: cs/0610003 · arxiv_version: cs/0610003v2 · doi: 10.48550/arxiv.cs/0610003 · pith_short_12: HMDAHOAQCYQK · pith_short_16: HMDAHOAQCYQK6JM2 · pith_short_8: HMDAHOAQ

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/HMDAHOAQCYQK6JM2L4YEPOE7E5 \
  | 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: 3b0603b8101620af259a5f3047b89f274ac3b3bbee9351291e535f7d0db5cf96

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "44e460a2a048023bc52062e9718131133ab883429f32c7db6eedd920ea6add65",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "cs.DM",
    "submitted_at": "2006-10-01T10:58:06Z",
    "title_canon_sha256": "e13e7ecb9f202231d6476f117d7c0b0c0d843b02c05607a069d60a3dcc6ee10e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "cs/0610003",
    "kind": "arxiv",
    "version": 2
  }
}