Pith Number

pith:XBCFPFH2

pith:2016:XBCFPFH2MNUGFUHOQAL2XQCT55

not attested not anchored not stored refs pending

A Direct Proof of Schwichtenberg's Bar Recursion Closure Theorem

Paulo Oliva, Silvia Steila

arxiv:1607.05237 v4 · 2016-07-18 · math.LO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{XBCFPFH2MNUGFUHOQAL2XQCT55}

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	2026-05-18T00:38:04.358930Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b8445794fa636862d0ee8017abc053ef52535a165705aeab75d9963b5f69116b

Aliases

arxiv: 1607.05237 · arxiv_version: 1607.05237v4 · doi: 10.48550/arxiv.1607.05237 · pith_short_12: XBCFPFH2MNUG · pith_short_16: XBCFPFH2MNUGFUHO · pith_short_8: XBCFPFH2

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/XBCFPFH2MNUGFUHOQAL2XQCT55 \
  | 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: b8445794fa636862d0ee8017abc053ef52535a165705aeab75d9963b5f69116b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9bd3312cb0df3b310374832e3785bf6550a60a6fd02afbdb3ef8b5a35e8b7fa2",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.LO",
    "submitted_at": "2016-07-18T18:46:14Z",
    "title_canon_sha256": "70aed797d65fcffcb01b6838a2d34b75d5129f55dad6f243101a5ed67572b194"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1607.05237",
    "kind": "arxiv",
    "version": 4
  }
}