Pith Number

pith:DEUK4PZJ

pith:2015:DEUK4PZJXXFDM37MOWVM5H7P7E

not attested not anchored not stored refs pending

Volume of Metric Balls in High-Dimensional Complex Grassmann Manifolds

Jukka Corander, Lu wei, Olav Tirkkonen, Renaud-Alexandre Pitaval

arxiv:1508.00256 v1 · 2015-08-02 · cs.IT · math.IT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{DEUK4PZJXXFDM37MOWVM5H7P7E}

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	2026-05-18T01:35:58.602309Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1928ae3f29bdca366fec75aace9feff916a3f7a34903d961c485a3a2c0589118

Aliases

arxiv: 1508.00256 · arxiv_version: 1508.00256v1 · doi: 10.48550/arxiv.1508.00256 · pith_short_12: DEUK4PZJXXFD · pith_short_16: DEUK4PZJXXFDM37M · pith_short_8: DEUK4PZJ

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/DEUK4PZJXXFDM37MOWVM5H7P7E \
  | 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: 1928ae3f29bdca366fec75aace9feff916a3f7a34903d961c485a3a2c0589118

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "cd4b284492fc82966778a238f542f0e15e6d3b21888856c5e3d14d7a2ae6321c",
    "cross_cats_sorted": [
      "math.IT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.IT",
    "submitted_at": "2015-08-02T16:36:14Z",
    "title_canon_sha256": "99f92821d081ce0f48a6a38bf8774c39cfe4d97cea056d1c1a950557eaec1df9"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1508.00256",
    "kind": "arxiv",
    "version": 1
  }
}