Pith Number

pith:WK2NHGDO

pith:2015:WK2NHGDONDCB6ZSZMWBTAQLWV2

not attested not anchored not stored refs pending

Non-displaceable toric fibers on compact toric manifolds via tropicalizations

Jaeho Lee, Yoosik Kim

arxiv:1507.06132 v1 · 2015-07-22 · math.SG · 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{WK2NHGDONDCB6ZSZMWBTAQLWV2}

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	2026-05-18T01:36:26.617041Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b2b4d3986e68c41f66596583304176aeb11fdad3df42612c6e87e84ef59f26f6

Aliases

arxiv: 1507.06132 · arxiv_version: 1507.06132v1 · doi: 10.48550/arxiv.1507.06132 · pith_short_12: WK2NHGDONDCB · pith_short_16: WK2NHGDONDCB6ZSZ · pith_short_8: WK2NHGDO

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/WK2NHGDONDCB6ZSZMWBTAQLWV2 \
  | 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: b2b4d3986e68c41f66596583304176aeb11fdad3df42612c6e87e84ef59f26f6

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "183ec8e17d4146768fbcc1d192bfe73f0775c034c5d753304bba55ed77512f2e",
    "cross_cats_sorted": [
      "math.AG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.SG",
    "submitted_at": "2015-07-22T11:19:36Z",
    "title_canon_sha256": "dec25843d74f2efc82f453f4aca8ba6c031f076d96dbee59200840a3185d0b18"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1507.06132",
    "kind": "arxiv",
    "version": 1
  }
}