Pith Number

pith:72WM65HA

pith:2015:72WM65HA6YWEP27OVEKB6IMSW4

not attested not anchored not stored refs pending

Entropy numbers of spheres in Banach and quasi-Banach spaces

Aicke Hinrichs, Sebastian Mayer

arxiv:1501.03680 v2 · 2015-01-15 · math.NA · math.FA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{72WM65HA6YWEP27OVEKB6IMSW4}

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	2026-05-18T02:17:11.340004Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

feaccf74e0f62c47ebeea9141f2192b72c3678e142ff0bebc56fa9cbecf72c54

Aliases

arxiv: 1501.03680 · arxiv_version: 1501.03680v2 · doi: 10.48550/arxiv.1501.03680 · pith_short_12: 72WM65HA6YWE · pith_short_16: 72WM65HA6YWEP27O · pith_short_8: 72WM65HA

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/72WM65HA6YWEP27OVEKB6IMSW4 \
  | 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: feaccf74e0f62c47ebeea9141f2192b72c3678e142ff0bebc56fa9cbecf72c54

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "68ec35d14f430f953cbda3a23145cb47a933361f36134d72c97975aa41e4227a",
    "cross_cats_sorted": [
      "math.FA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NA",
    "submitted_at": "2015-01-15T13:50:32Z",
    "title_canon_sha256": "575bbbc8adf9002e76c9cdf8fb1a5b5273ab0e07cedf20f3bc3fb10536aaa3f7"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1501.03680",
    "kind": "arxiv",
    "version": 2
  }
}