Pith Number

pith:2FGYOO4C

pith:2016:2FGYOO4CWMFLADNEIQGBEEXG3K

not attested not anchored not stored refs pending

Multiplicity results and sign changing solutions of non-local equations with concave-convex nonlinearities

Debangana Mukherjee, Mousomi Bhakta

arxiv:1603.05554 v2 · 2016-03-17 · 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{2FGYOO4CWMFLADNEIQGBEEXG3K}

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	2026-05-17T23:54:57.142223Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d14d873b82b30ab00da4440c1212e6da87e3323a2f887a6251e73e3335670b6a

Aliases

arxiv: 1603.05554 · arxiv_version: 1603.05554v2 · doi: 10.48550/arxiv.1603.05554 · pith_short_12: 2FGYOO4CWMFL · pith_short_16: 2FGYOO4CWMFLADNE · pith_short_8: 2FGYOO4C

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/2FGYOO4CWMFLADNEIQGBEEXG3K \
  | 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: d14d873b82b30ab00da4440c1212e6da87e3323a2f887a6251e73e3335670b6a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "cf399716303ba6c103f93c9c16850981b7f58804deb224e1c12a521494ccc35e",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2016-03-17T16:08:17Z",
    "title_canon_sha256": "63a03e4f0c87907599c3b6fbbb4573fb2870f370b252f73d3e011ae276c79694"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1603.05554",
    "kind": "arxiv",
    "version": 2
  }
}