Pith Number

pith:AZLB7NKG

pith:2015:AZLB7NKGZZUUO247RPJK5THOWI

not attested not anchored not stored refs pending

Degeneration of Linear Series From the Tropical Point of View and Applications

David Jensen, Matthew Baker

arxiv:1504.05544 v2 · 2015-04-21 · math.AG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{AZLB7NKGZZUUO247RPJK5THOWI}

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	2026-05-18T01:33:51.667299Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

06561fb546ce69476b9f8bd2aecceeb20f49949b9f611a91d7a1c7d790d710a4

Aliases

arxiv: 1504.05544 · arxiv_version: 1504.05544v2 · doi: 10.48550/arxiv.1504.05544 · pith_short_12: AZLB7NKGZZUU · pith_short_16: AZLB7NKGZZUUO247 · pith_short_8: AZLB7NKG

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/AZLB7NKGZZUUO247RPJK5THOWI \
  | 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: 06561fb546ce69476b9f8bd2aecceeb20f49949b9f611a91d7a1c7d790d710a4

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "bb18cac6731b9282e3edf68b12ac822cc368608b7701cfa7f4c9c0f00956eab7",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2015-04-21T18:40:48Z",
    "title_canon_sha256": "fb210213c2ed663ba4cd657425d692655050db6c514a1e464ebcd4c7e2ea23a0"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1504.05544",
    "kind": "arxiv",
    "version": 2
  }
}