Pith Number

pith:NDM25FWX

pith:2012:NDM25FWXK5ZWBFJGV77ZGFWIC3

not attested not anchored not stored refs pending

Computing medians and means in Hadamard spaces

Miroslav Bacak

arxiv:1210.2145 v3 · 2012-10-08 · math.MG · q-bio.QM

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{NDM25FWXK5ZWBFJGV77ZGFWIC3}

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	2026-05-18T02:49:02.378599Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

68d9ae96d75773609526afff9316c816d58d6a662422a8a4ca2b8fdad6664e33

Aliases

arxiv: 1210.2145 · arxiv_version: 1210.2145v3 · doi: 10.48550/arxiv.1210.2145 · pith_short_12: NDM25FWXK5ZW · pith_short_16: NDM25FWXK5ZWBFJG · pith_short_8: NDM25FWX

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/NDM25FWXK5ZWBFJGV77ZGFWIC3 \
  | 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: 68d9ae96d75773609526afff9316c816d58d6a662422a8a4ca2b8fdad6664e33

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "758fac577301ca49530bdfa3b52a5e9083bc942af49207f837a4b3edbfcc0778",
    "cross_cats_sorted": [
      "q-bio.QM"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.MG",
    "submitted_at": "2012-10-08T05:12:17Z",
    "title_canon_sha256": "1fafe62af14fe735a03ffd9cd25a1cd9a6e33b9d8ac6a9f4e8c0fb29b6f57c24"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1210.2145",
    "kind": "arxiv",
    "version": 3
  }
}