Pith Number

pith:EPCXAVFM

pith:2016:EPCXAVFMDX5UQP3QSL3GJ2KVSK

not attested not anchored not stored refs pending

Spiked solutions for Schr\"odinger systems with Sobolev critical exponent: the cases of competitive and weakly cooperative interactions

Angela Pistoia, Hugo Tavares

arxiv:1605.03776 v1 · 2016-05-12 · 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{EPCXAVFMDX5UQP3QSL3GJ2KVSK}

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	2026-05-18T01:14:59.513596Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

23c57054ac1dfb483f7092f664e955929f99632125ea7d86aa11f094f1ee9a0b

Aliases

arxiv: 1605.03776 · arxiv_version: 1605.03776v1 · doi: 10.48550/arxiv.1605.03776 · pith_short_12: EPCXAVFMDX5U · pith_short_16: EPCXAVFMDX5UQP3Q · pith_short_8: EPCXAVFM

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/EPCXAVFMDX5UQP3QSL3GJ2KVSK \
  | 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: 23c57054ac1dfb483f7092f664e955929f99632125ea7d86aa11f094f1ee9a0b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0d5653b595843e7280da09af476b0604c03abcf50d3eecd3f9c28cb6ef11ae0f",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2016-05-12T12:00:43Z",
    "title_canon_sha256": "20d24a9d5466ae451bfdf957948862587f6621f5a25ee20719d8344a334b759a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1605.03776",
    "kind": "arxiv",
    "version": 1
  }
}