Pith Number

pith:TBC3VTDM

pith:2016:TBC3VTDM2R4UZ2GIEGOMO4R66F

not attested not anchored not stored refs pending

Rank of tropical curves and tropical hypersurfaces

Boaz Elazar

arxiv:1603.09168 v2 · 2016-03-30 · 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{TBC3VTDM2R4UZ2GIEGOMO4R66F}

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	2026-05-18T00:14:16.733420Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9845bacc6cd4794ce8c8219cc7723ef15642010b89388c04bc299cf06e5d3203

Aliases

arxiv: 1603.09168 · arxiv_version: 1603.09168v2 · doi: 10.48550/arxiv.1603.09168 · pith_short_12: TBC3VTDM2R4U · pith_short_16: TBC3VTDM2R4UZ2GI · pith_short_8: TBC3VTDM

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/TBC3VTDM2R4UZ2GIEGOMO4R66F \
  | 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: 9845bacc6cd4794ce8c8219cc7723ef15642010b89388c04bc299cf06e5d3203

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "19d8685d7d5ef46ce49d7a50bcf770367ff86577cdc5caa36f018fdc1b72564e",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2016-03-30T13:06:22Z",
    "title_canon_sha256": "7844dac73fc930643b46f1324d8cb269d3d02b70c972568dd4023a3facd1a6d4"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1603.09168",
    "kind": "arxiv",
    "version": 2
  }
}