Pith Number

pith:JLITZCSE

pith:2009:JLITZCSE7H4VOCHUYGY6F4UXHG

not attested not anchored not stored refs pending

The real field with an irrational power function and a dense multiplicative subgroup

Philipp Hieronymi

arxiv:0912.2469 v1 · 2009-12-13 · 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{JLITZCSE7H4VOCHUYGY6F4UXHG}

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	2026-05-18T04:27:57.182784Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

4ad13c8a44f9f95708f4c1b1e2f29739bcfaee5a32dbe24a04519fdbe7c1148d

Aliases

arxiv: 0912.2469 · arxiv_version: 0912.2469v1 · doi: 10.48550/arxiv.0912.2469 · pith_short_12: JLITZCSE7H4V · pith_short_16: JLITZCSE7H4VOCHU · pith_short_8: JLITZCSE

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/JLITZCSE7H4VOCHUYGY6F4UXHG \
  | 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: 4ad13c8a44f9f95708f4c1b1e2f29739bcfaee5a32dbe24a04519fdbe7c1148d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "476ab65e3da7555b3ba1d1e2d08dc5201aca7360995b1bae0dbb39a44ff9d18f",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.LO",
    "submitted_at": "2009-12-13T02:11:09Z",
    "title_canon_sha256": "6bd2188a9a56f7497f6897a148b085829b0f9a636b21a81f83af02fc2d346b9a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0912.2469",
    "kind": "arxiv",
    "version": 1
  }
}