Pith Number

pith:64YLF422

pith:2007:64YLF422S42VOAIBVJS2TFK6PL

not attested not anchored not stored refs pending

Positive toric fibrations

Misha Verbitsky

arxiv:math/0703162 v3 · 2007-03-06 · math.AG · math.CV · 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{64YLF422S42VOAIBVJS2TFK6PL}

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	2026-05-18T02:57:45.238364Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f730b2f35a9735570101aa65a9955e7ac69c917379760327406778a491634db2

Aliases

arxiv: math/0703162 · arxiv_version: math/0703162v3 · doi: 10.48550/arxiv.math/0703162 · pith_short_12: 64YLF422S42V · pith_short_16: 64YLF422S42VOAIB · pith_short_8: 64YLF422

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/64YLF422S42VOAIBVJS2TFK6PL \
  | 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: f730b2f35a9735570101aa65a9955e7ac69c917379760327406778a491634db2

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f76b71cb5de1daec78502e1a2d54e05e2b7de19a0f9f0c35c03437d6c8b16603",
    "cross_cats_sorted": [
      "math.CV",
      "math.DG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2007-03-06T16:41:30Z",
    "title_canon_sha256": "8266fc377acfffa669b60d18c8407aae85eb6a0f784513242b32f54f1150179e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0703162",
    "kind": "arxiv",
    "version": 3
  }
}