Pith Number

pith:X3LQZIE5

pith:2016:X3LQZIE5S4Q4DLF6IMG47MQMGH

not attested not anchored not stored refs pending

Non-existence of solutions for a mean field equation on flat tori at critical parameter $16\pi$

Chang-shou Lin, Ting-Jung Kuo, Zhijie Chen

arxiv:1610.01787 v2 · 2016-10-06 · 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{X3LQZIE5S4Q4DLF6IMG47MQMGH}

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	2026-05-18T00:40:13.699634Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

bed70ca09d9721c1acbe430dcfb20c31d4be12480f66f763bc5267b573d0c8ea

Aliases

arxiv: 1610.01787 · arxiv_version: 1610.01787v2 · doi: 10.48550/arxiv.1610.01787 · pith_short_12: X3LQZIE5S4Q4 · pith_short_16: X3LQZIE5S4Q4DLF6 · pith_short_8: X3LQZIE5

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/X3LQZIE5S4Q4DLF6IMG47MQMGH \
  | 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: bed70ca09d9721c1acbe430dcfb20c31d4be12480f66f763bc5267b573d0c8ea

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "263068586e0384bc835d4be12ba089546ae4f2c4336717838663c8123637e0b5",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2016-10-06T09:27:51Z",
    "title_canon_sha256": "eee98bff4b16cfa6ea42247a527aa41b0023e2691ed7f197fdc94a871bbcff5c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1610.01787",
    "kind": "arxiv",
    "version": 2
  }
}