Pith Number

pith:2UAPYYAA

pith:2015:2UAPYYAAEXQWM5RI2INH5CVXVM

not attested not anchored not stored refs pending

Tropical Hopf manifolds and contracting germs

Kristin Shaw, Matteo Ruggiero

arxiv:1509.03787 v1 · 2015-09-13 · math.AG · math.DS

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{2UAPYYAAEXQWM5RI2INH5CVXVM}

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	2026-05-18T01:33:14.543082Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d500fc600025e1667628d21a7e8ab7ab3d781950ba008e03b22befb2b6928b6b

Aliases

arxiv: 1509.03787 · arxiv_version: 1509.03787v1 · doi: 10.48550/arxiv.1509.03787 · pith_short_12: 2UAPYYAAEXQW · pith_short_16: 2UAPYYAAEXQWM5RI · pith_short_8: 2UAPYYAA

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/2UAPYYAAEXQWM5RI2INH5CVXVM \
  | 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: d500fc600025e1667628d21a7e8ab7ab3d781950ba008e03b22befb2b6928b6b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c0070fbf8b95b4c5b4e72d4935f09ca7f467d3ce8aab1bfb337642d2b5121de3",
    "cross_cats_sorted": [
      "math.DS"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2015-09-13T00:01:04Z",
    "title_canon_sha256": "e90fc2dc3bcfa52b57fa58f5b2f531991d8c2221f4e3efa552fb43401a649e96"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1509.03787",
    "kind": "arxiv",
    "version": 1
  }
}