Pith Number

pith:7KB7IXSQ

pith:2021:7KB7IXSQYW73UAL7U7XMOROAC7

not attested not anchored not stored refs pending

Range decreasing group homomorphisms and holomorphic maps between generalized loop spaces

Ning Zhang

arxiv:2102.06157 v1 · 2021-02-11 · math.CV · math.FA · math.RT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{7KB7IXSQYW73UAL7U7XMOROAC7}

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	2026-07-05T04:40:06.606045Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

fa83f45e50c5bfba017fa7eec745c017c3ffc063a41fecd6fa3601848cfe2840

Aliases

arxiv: 2102.06157 · arxiv_version: 2102.06157v1 · doi: 10.48550/arxiv.2102.06157 · pith_short_12: 7KB7IXSQYW73 · pith_short_16: 7KB7IXSQYW73UAL7 · pith_short_8: 7KB7IXSQ

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/7KB7IXSQYW73UAL7U7XMOROAC7 \
  | 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: fa83f45e50c5bfba017fa7eec745c017c3ffc063a41fecd6fa3601848cfe2840

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "279b36f9e80c2b65b7a9d30741adf34124489e80790b322dea1c5a8431170b56",
    "cross_cats_sorted": [
      "math.FA",
      "math.RT"
    ],
    "license": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
    "primary_cat": "math.CV",
    "submitted_at": "2021-02-11T17:59:29Z",
    "title_canon_sha256": "a36646088b65656c7503fcb393356a977b2fa007c659f09c21e500a47e6781d8"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2102.06157",
    "kind": "arxiv",
    "version": 1
  }
}