Pith Number

pith:GTIBZ5ID

pith:2023:GTIBZ5ID73GHPEZIMV7DHRTKMZ

not attested not anchored not stored refs pending

A proof for Ando's theorem on norm-coherent coordinates via the Coleman norm operator

Hongxiang Zhao

arxiv:2310.09837 v1 · 2023-10-15 · math.AT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{GTIBZ5ID73GHPEZIMV7DHRTKMZ}

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	2026-07-05T07:01:11.805223Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

34d01cf503fecc779328657e33c66a667f1fed397bdde00898c7d1ffe9c4e13a

Aliases

arxiv: 2310.09837 · arxiv_version: 2310.09837v1 · doi: 10.48550/arxiv.2310.09837 · pith_short_12: GTIBZ5ID73GH · pith_short_16: GTIBZ5ID73GHPEZI · pith_short_8: GTIBZ5ID

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/GTIBZ5ID73GHPEZIMV7DHRTKMZ \
  | 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: 34d01cf503fecc779328657e33c66a667f1fed397bdde00898c7d1ffe9c4e13a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "50115d6457335466138ad44812cf5ae5758a84ae62b687bca5aabe28a77b1000",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.AT",
    "submitted_at": "2023-10-15T13:51:18Z",
    "title_canon_sha256": "bd534a4ed5624b3cb5e97c94b4979325ba2c53dc4349c0738a02c3923b473934"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2310.09837",
    "kind": "arxiv",
    "version": 1
  }
}