Pith Number

pith:Z7J6PGIJ

pith:2018:Z7J6PGIJJFPK26FJVQ6M35J7LP

not attested not anchored not stored refs pending

Harmonic morphisms of Allof-Wallach spaces of positive curvature

Hajime Urakawa

arxiv:1809.10817 v1 · 2018-09-28 · math.DG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{Z7J6PGIJJFPK26FJVQ6M35J7LP}

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	2026-05-18T00:04:33.788425Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

cfd3e79909495ead78a9ac3ccdf53f5bdcd2159834562385ca69eef401348f7b

Aliases

arxiv: 1809.10817 · arxiv_version: 1809.10817v1 · doi: 10.48550/arxiv.1809.10817 · pith_short_12: Z7J6PGIJJFPK · pith_short_16: Z7J6PGIJJFPK26FJ · pith_short_8: Z7J6PGIJ

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/Z7J6PGIJJFPK26FJVQ6M35J7LP \
  | 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: cfd3e79909495ead78a9ac3ccdf53f5bdcd2159834562385ca69eef401348f7b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1c300aefed709467b2de91e720160324fe24bb2277fadfc7e6208eb7bfce1e08",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2018-09-28T01:42:20Z",
    "title_canon_sha256": "48e4e67a07c25bed8debedafc24f32ab0bb6c9d6b4189e83b81bd61d0435078a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1809.10817",
    "kind": "arxiv",
    "version": 1
  }
}