Pith Number

pith:WL32NW43

pith:2016:WL32NW43FJ7PQFMKY6T3BBBPS5

not attested not anchored not stored refs pending

On the existence of infinitely many closed geodesics on non-compact manifolds

Luca Asselle, Marco Mazzucchelli

arxiv:1602.03679 v2 · 2016-02-11 · math.DG · math.SG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{WL32NW43FJ7PQFMKY6T3BBBPS5}

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	2026-05-18T00:48:28.481197Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b2f7a6db9b2a7ef8158ac7a7b0842f974d74d365e0358567899deaa7a85644ad

Aliases

arxiv: 1602.03679 · arxiv_version: 1602.03679v2 · doi: 10.48550/arxiv.1602.03679 · pith_short_12: WL32NW43FJ7P · pith_short_16: WL32NW43FJ7PQFMK · pith_short_8: WL32NW43

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/WL32NW43FJ7PQFMKY6T3BBBPS5 \
  | 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: b2f7a6db9b2a7ef8158ac7a7b0842f974d74d365e0358567899deaa7a85644ad

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "453249858025cd9af4fc4be0d2cf8d595c3758fadba5dfe4442097601bf89943",
    "cross_cats_sorted": [
      "math.SG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2016-02-11T11:21:36Z",
    "title_canon_sha256": "81d4e2b866707fd75ded468651fcc8e9e9a01cfa1c7a639ec425a7cf1e4ee166"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1602.03679",
    "kind": "arxiv",
    "version": 2
  }
}