Pith Number

pith:W33VVFZD

pith:2018:W33VVFZDZXF6EDZV7PBFM7M5AF

not attested not anchored not stored refs pending

Sup norm on $\text{PGL}_n$ in depth aspect

Yueke Hu

arxiv:1809.00617 v1 · 2018-09-03 · 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{W33VVFZDZXF6EDZV7PBFM7M5AF}

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	2026-05-18T00:06:33.010261Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b6f75a9723cdcbe20f35fbc2567d9d0144c9bfbad7befb3f09b6ce2166c4de29

Aliases

arxiv: 1809.00617 · arxiv_version: 1809.00617v1 · doi: 10.48550/arxiv.1809.00617 · pith_short_12: W33VVFZDZXF6 · pith_short_16: W33VVFZDZXF6EDZV · pith_short_8: W33VVFZD

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/W33VVFZDZXF6EDZV7PBFM7M5AF \
  | 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: b6f75a9723cdcbe20f35fbc2567d9d0144c9bfbad7befb3f09b6ce2166c4de29

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b3a99cdf576107fd0eb3d1f00131c89604deb3d9e2dc35e3c89fd544af290a73",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2018-09-03T14:30:00Z",
    "title_canon_sha256": "ce0445fe45f23b9de163c87810225fdee9569c6d2712f103afb622c8e5cbabb5"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1809.00617",
    "kind": "arxiv",
    "version": 1
  }
}