Pith Number

pith:T73L45UA

pith:2011:T73L45UAG7KUBF5KJYNGDCT7QO

not attested not anchored not stored refs pending

Threshold solutions in the case of mass-shift for the critical Kline-Gordon equation

Kenji Nakanishi, Nader Masmoudi, Slim Ibrahim

arxiv:1110.1709 v1 · 2011-10-08 · 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{T73L45UAG7KUBF5KJYNGDCT7QO}

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	2026-05-18T04:11:19.800913Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9ff6be768037d54097aa4e1a618a7f838d8d87bffd9c55affdb6be8a1cfc1550

Aliases

arxiv: 1110.1709 · arxiv_version: 1110.1709v1 · doi: 10.48550/arxiv.1110.1709 · pith_short_12: T73L45UAG7KU · pith_short_16: T73L45UAG7KUBF5K · pith_short_8: T73L45UA

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/T73L45UAG7KUBF5KJYNGDCT7QO \
  | 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: 9ff6be768037d54097aa4e1a618a7f838d8d87bffd9c55affdb6be8a1cfc1550

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1638f2b409a6c2fd5fb6dc613a11125df488d8ab4bcc60a933f9a69b68d0c659",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2011-10-08T08:45:57Z",
    "title_canon_sha256": "47eb2e92e235292764c1f1e9951f746020d8c8713b33e4ca85cdad6b542211d3"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1110.1709",
    "kind": "arxiv",
    "version": 1
  }
}