Pith Number

pith:VRHV22Z5

pith:2018:VRHV22Z54DBUSEEH2BERBM3WXI

not attested not anchored not stored refs pending

Dynamical models for Liouville and obstructions to further progress on sign patterns

Will Sawin

arxiv:1809.03280 v1 · 2018-09-10 · math.NT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{VRHV22Z54DBUSEEH2BERBM3WXI}

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	2026-05-18T00:06:09.379247Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ac4f5d6b3de0c3491087d04910b376ba2aab699b4297ea2d10dc8f263568ad69

Aliases

arxiv: 1809.03280 · arxiv_version: 1809.03280v1 · doi: 10.48550/arxiv.1809.03280 · pith_short_12: VRHV22Z54DBU · pith_short_16: VRHV22Z54DBUSEEH · pith_short_8: VRHV22Z5

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/VRHV22Z54DBUSEEH2BERBM3WXI \
  | 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: ac4f5d6b3de0c3491087d04910b376ba2aab699b4297ea2d10dc8f263568ad69

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7c271668d70df5d5405dc03f58287a01bc9fdca30e91e67f4a140aa374905b2e",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2018-09-10T12:56:23Z",
    "title_canon_sha256": "c814dce4ce2657c997993883187334365592838d847d7de67ffad71f121fb260"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1809.03280",
    "kind": "arxiv",
    "version": 1
  }
}