Pith Number

pith:X2PCJDRE

pith:2026:X2PCJDREC7WXALBH2GKNO2UPWQ

not attested not anchored not stored refs pending

Weakly o-minimal fields have the exchange property but not generic differentiability

Will Johnson

arxiv:2606.08527 v1 · 2026-06-07 · 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{X2PCJDREC7WXALBH2GKNO2UPWQ}

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	2026-06-09T01:05:39.096825Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

be9e248e2417ed702c27d194d76a8fb40ee8c2bcef622aa2f4030dce0fa1ec99

Aliases

arxiv: 2606.08527 · arxiv_version: 2606.08527v1 · doi: 10.48550/arxiv.2606.08527 · pith_short_12: X2PCJDREC7WX · pith_short_16: X2PCJDREC7WXALBH · pith_short_8: X2PCJDRE

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/X2PCJDREC7WXALBH2GKNO2UPWQ \
  | 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: be9e248e2417ed702c27d194d76a8fb40ee8c2bcef622aa2f4030dce0fa1ec99

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6cae4b3be12e45a749aea8e6ccdd4c42a939924f8560d582ae00e4d06afa7530",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.LO",
    "submitted_at": "2026-06-07T09:11:43Z",
    "title_canon_sha256": "f0ee9fd29bbe1292a127c9f33c331009f66ad53b39f0b985d7baa7f918ac4753"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.08527",
    "kind": "arxiv",
    "version": 1
  }
}