Pith Number

pith:SMUUXDAW

pith:2014:SMUUXDAWIV3LRB36346HGSSJZ2

not attested not anchored not stored refs pending

Monotonicity of the first Dirichlet eigenvalue of the Laplacian on manifolds of nonpositive curvature

Jesse Ratzkin, Tom Carroll

arxiv:1407.0864 v1 · 2014-07-03 · math.AP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{SMUUXDAWIV3LRB36346HGSSJZ2}

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	2026-05-18T01:12:20.093678Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

93294b8c164576b8877edf3c734a49ce867076ad8b957f333752a4b226b1b05e

Aliases

arxiv: 1407.0864 · arxiv_version: 1407.0864v1 · doi: 10.48550/arxiv.1407.0864 · pith_short_12: SMUUXDAWIV3L · pith_short_16: SMUUXDAWIV3LRB36 · pith_short_8: SMUUXDAW

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/SMUUXDAWIV3LRB36346HGSSJZ2 \
  | 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: 93294b8c164576b8877edf3c734a49ce867076ad8b957f333752a4b226b1b05e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f0687fc931f93bc0bb3c64bf4610d7eef69b50a80a5e2996c6855419022d091c",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2014-07-03T11:01:35Z",
    "title_canon_sha256": "fb1f974e9e3e2f3dfa4bf428b76aed97c6d83b44203bb1b9adfba545e919431f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1407.0864",
    "kind": "arxiv",
    "version": 1
  }
}