Pith Number

pith:ZH4HU4GR

pith:2014:ZH4HU4GRCF2BDF3X67MEUGGMG7

not attested not anchored not stored refs pending

Infinitely many sign changing solutions of an elliptic problem involving critical Sobolev and Hardy-Sobolev exponent

Mousomi Bhakta

arxiv:1410.7880 v1 · 2014-10-29 · 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{ZH4HU4GRCF2BDF3X67MEUGGMG7}

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	2026-05-18T02:39:07.980213Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c9f87a70d11174119777f7d84a18cc37d79f4782618bd164594bed2b505548c3

Aliases

arxiv: 1410.7880 · arxiv_version: 1410.7880v1 · doi: 10.48550/arxiv.1410.7880 · pith_short_12: ZH4HU4GRCF2B · pith_short_16: ZH4HU4GRCF2BDF3X · pith_short_8: ZH4HU4GR

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/ZH4HU4GRCF2BDF3X67MEUGGMG7 \
  | 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: c9f87a70d11174119777f7d84a18cc37d79f4782618bd164594bed2b505548c3

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "90bc842ad2a5e2afff61e6a30766fe47bb3ff32f773636c861086ed66fbfbc15",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2014-10-29T05:43:44Z",
    "title_canon_sha256": "53bb3368f53b670044d6d2b7f4f0dc6d2ab701b6035f7328fd3bb7395081ff9d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1410.7880",
    "kind": "arxiv",
    "version": 1
  }
}