Pith Number

pith:MYZ3MT7L

pith:2019:MYZ3MT7LCSGWUA5QRT2RTNYKHV

not attested not anchored not stored refs pending

Singular periodic solutions to a critical equation in the Heisenberg group

Claudio Afeltra

arxiv:1908.02264 v2 · 2019-08-06 · 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{MYZ3MT7LCSGWUA5QRT2RTNYKHV}

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	2026-07-05T01:00:32.895461Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6633b64feb148d6a03b08cf519b70a3d56ce69606f91a58b0d2d01109d3ec67d

Aliases

arxiv: 1908.02264 · arxiv_version: 1908.02264v2 · doi: 10.48550/arxiv.1908.02264 · pith_short_12: MYZ3MT7LCSGW · pith_short_16: MYZ3MT7LCSGWUA5Q · pith_short_8: MYZ3MT7L

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/MYZ3MT7LCSGWUA5QRT2RTNYKHV \
  | 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: 6633b64feb148d6a03b08cf519b70a3d56ce69606f91a58b0d2d01109d3ec67d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1c89650c3a4f39e0ccf88db0eef6ef4d03420fd71abb325992b8e09ac1c102e8",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2019-08-06T17:28:07Z",
    "title_canon_sha256": "3e9b4373c5300446af96d1619e053b5cb2c8516ca53fe6998dd7235cf7406072"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1908.02264",
    "kind": "arxiv",
    "version": 2
  }
}