Pith Number

pith:4X7YPHTH

pith:2021:4X7YPHTHQVA6A2XDFKUZXLOTXG

not attested not anchored not stored refs pending

Normalized solutions to a class of Kirchhoff equations with Sobolev critical exponent

Gongbao LI, Tao Yang, Xiao Luo

arxiv:2103.08106 v1 · 2021-03-15 · 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{4X7YPHTHQVA6A2XDFKUZXLOTXG}

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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.

Cited by

1 paper in Pith

Multiplicity and asymptotic behavior of normalized solutions to p-Kirchhoff equations

Receipt and verification

First computed	2026-07-05T02:22:47.922769Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e5ff879e678541e06ae32aa99badd3b9bb887d1aedbabf31e5e5660e660ed3ba

Aliases

arxiv: 2103.08106 · arxiv_version: 2103.08106v1 · doi: 10.48550/arxiv.2103.08106 · pith_short_12: 4X7YPHTHQVA6 · pith_short_16: 4X7YPHTHQVA6A2XD · pith_short_8: 4X7YPHTH

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/4X7YPHTHQVA6A2XDFKUZXLOTXG \
  | 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: e5ff879e678541e06ae32aa99badd3b9bb887d1aedbabf31e5e5660e660ed3ba

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e5af58ddb619ee0b6fb69d023e19b4cc35b3f4115190ca7237117564707db02b",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2021-03-15T03:00:53Z",
    "title_canon_sha256": "5aae275f70c8848fd4e0513d42d956028db42329bd41ecf96f9a8db3ed593d56"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2103.08106",
    "kind": "arxiv",
    "version": 1
  }
}