Pith Number

pith:HBP3YN77

pith:2013:HBP3YN77WQFIJHYO24EIIP4WJ4

not attested not anchored not stored refs pending

Birkhoff's version of Hilbert's metric and its applications in analysis

Bas Lemmens, Roger Nussbaum

arxiv:1304.7921 v1 · 2013-04-30 · math.MG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{HBP3YN77WQFIJHYO24EIIP4WJ4}

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	2026-05-18T03:26:51.387075Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

385fbc37ffb40a849f0ed708843f964f2c5646ce9e1473f5adb7ee3a4d709dc5

Aliases

arxiv: 1304.7921 · arxiv_version: 1304.7921v1 · doi: 10.48550/arxiv.1304.7921 · pith_short_12: HBP3YN77WQFI · pith_short_16: HBP3YN77WQFIJHYO · pith_short_8: HBP3YN77

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/HBP3YN77WQFIJHYO24EIIP4WJ4 \
  | 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: 385fbc37ffb40a849f0ed708843f964f2c5646ce9e1473f5adb7ee3a4d709dc5

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "302f268b70065a3f20d0aed921f6b3f4846c5796c9f2d18c473ccc28872550e4",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.MG",
    "submitted_at": "2013-04-30T09:00:09Z",
    "title_canon_sha256": "4cbe7d94dbcbe9c4b07b149164ad0b86ec401df52026dbeacdf4c00831f29a9f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1304.7921",
    "kind": "arxiv",
    "version": 1
  }
}