Pith Number

pith:SO72UKC5

pith:2015:SO72UKC5OYMIRVKVSP5OFVXUPP

not attested not anchored not stored refs pending

An extension problem for sums of fractional Laplacians and 1-D symmetry of phase transitions

Joaquim Serra, Xavier Cabre

arxiv:1510.01596 v2 · 2015-10-06 · 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{SO72UKC5OYMIRVKVSP5OFVXUPP}

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	2026-05-18T01:24:18.108049Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

93bfaa285d761888d55593fae2d6f47be733a65beff3bac83ace05985fd9a4ff

Aliases

arxiv: 1510.01596 · arxiv_version: 1510.01596v2 · doi: 10.48550/arxiv.1510.01596 · pith_short_12: SO72UKC5OYMI · pith_short_16: SO72UKC5OYMIRVKV · pith_short_8: SO72UKC5

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/SO72UKC5OYMIRVKVSP5OFVXUPP \
  | 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: 93bfaa285d761888d55593fae2d6f47be733a65beff3bac83ace05985fd9a4ff

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e42ea367c82f11c3b2ba8883c8bb42bfc2fc5ba232a84d0c461d64054678d1dd",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2015-10-06T14:40:25Z",
    "title_canon_sha256": "175ac5ac1bd7d4b35404c7cb2beb60555b4d482260df98bf4f85f2c206a02846"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1510.01596",
    "kind": "arxiv",
    "version": 2
  }
}