Pith Number

pith:KYRECHJX

pith:2016:KYRECHJX2EQT4PPB6QHJR4OJAH

not attested not anchored not stored refs pending

The orthogonal complements of $H^1(\mathbb{R})$ in its regular Dirichlet extensions

Jiangang Ying, Liping Li, Yuncong Shen

arxiv:1611.06782 v1 · 2016-11-21 · math.PR

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{KYRECHJX2EQT4PPB6QHJR4OJAH}

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	2026-05-18T00:57:32.902966Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5622411d37d1213e3de1f40e98f1c901c1a1b86193b1cb69bee749f67cd51bef

Aliases

arxiv: 1611.06782 · arxiv_version: 1611.06782v1 · doi: 10.48550/arxiv.1611.06782 · pith_short_12: KYRECHJX2EQT · pith_short_16: KYRECHJX2EQT4PPB · pith_short_8: KYRECHJX

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/KYRECHJX2EQT4PPB6QHJR4OJAH \
  | 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: 5622411d37d1213e3de1f40e98f1c901c1a1b86193b1cb69bee749f67cd51bef

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0ff5f77a7f893251f6929102713ca260f664b3eeb9dc10bad02da1fbebd68a33",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2016-11-21T13:38:43Z",
    "title_canon_sha256": "95137bb51acd82eb844868739c660dc26316c2254ade388df4350ef1ba5a3855"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1611.06782",
    "kind": "arxiv",
    "version": 1
  }
}