Pith Number

pith:NLPPSTJN

pith:2018:NLPPSTJN4LLCD35HUUVGUUGQTI

not attested not anchored not stored refs pending

Bounds on the first Betti number - an approach via Schatten norm estimates on semigroup differences

Christian Rose, Marcel Hansmann, Peter Stollmann

arxiv:1810.12205 v1 · 2018-10-29 · math.DG · math-ph · math.MP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{NLPPSTJN4LLCD35HUUVGUUGQTI}

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	2026-05-18T00:02:03.929033Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6adef94d2de2d621efa7a52a6a50d09a19146b26fd4edee80d47bf9f925e7a6c

Aliases

arxiv: 1810.12205 · arxiv_version: 1810.12205v1 · doi: 10.48550/arxiv.1810.12205 · pith_short_12: NLPPSTJN4LLC · pith_short_16: NLPPSTJN4LLCD35H · pith_short_8: NLPPSTJN

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/NLPPSTJN4LLCD35HUUVGUUGQTI \
  | 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: 6adef94d2de2d621efa7a52a6a50d09a19146b26fd4edee80d47bf9f925e7a6c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "610294320408c956f74240a603bf92887fff30d21906500bc2711e67106fc06f",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2018-10-29T15:52:46Z",
    "title_canon_sha256": "abb78e2674873962c1b21bb10ad2de756103d00d656d63919fe95fb36f2e9ffb"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1810.12205",
    "kind": "arxiv",
    "version": 1
  }
}