Pith Number

pith:VG6MJQ4V

pith:2015:VG6MJQ4VGK77BB4R3U6XXFVRUI

not attested not anchored not stored refs pending

Multiple positive solutions for a superlinear problem: a topological approach

Fabio Zanolin, Guglielmo Feltrin

arxiv:1512.05128 v1 · 2015-12-16 · math.CA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{VG6MJQ4VGK77BB4R3U6XXFVRUI}

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	2026-05-18T01:24:13.419530Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a9bcc4c39532bff08791dd3d7b96b1a22bc6f06545e1fe72b21ad86c2e899185

Aliases

arxiv: 1512.05128 · arxiv_version: 1512.05128v1 · doi: 10.48550/arxiv.1512.05128 · pith_short_12: VG6MJQ4VGK77 · pith_short_16: VG6MJQ4VGK77BB4R · pith_short_8: VG6MJQ4V

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/VG6MJQ4VGK77BB4R3U6XXFVRUI \
  | 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: a9bcc4c39532bff08791dd3d7b96b1a22bc6f06545e1fe72b21ad86c2e899185

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0e51961cdc596b60003bade59a253776418b031a17e86ceab2c2fed1cddecddb",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2015-12-16T11:00:02Z",
    "title_canon_sha256": "830a6ce3c556cdbdf067b5d22b734f0d0048986023e8559b791b247592db5914"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1512.05128",
    "kind": "arxiv",
    "version": 1
  }
}