Pith Number

pith:PYEMM4JV

pith:2015:PYEMM4JVXXW6YCRE7FBDR5BPMS

not attested not anchored not stored refs pending

Product-Mix Auctions and Tropical Geometry

Josephine Yu, Ngoc Mai Tran

arxiv:1505.05737 v4 · 2015-05-15 · cs.GT · math.CO · q-fin.EC

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{PYEMM4JVXXW6YCRE7FBDR5BPMS}

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	2026-05-18T00:32:03.274637Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7e08c67135bdedec0a24f94238f42f6480e679824a895178246cec3979d0d8ba

Aliases

arxiv: 1505.05737 · arxiv_version: 1505.05737v4 · doi: 10.48550/arxiv.1505.05737 · pith_short_12: PYEMM4JVXXW6 · pith_short_16: PYEMM4JVXXW6YCRE · pith_short_8: PYEMM4JV

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/PYEMM4JVXXW6YCRE7FBDR5BPMS \
  | 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: 7e08c67135bdedec0a24f94238f42f6480e679824a895178246cec3979d0d8ba

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9b67561021b6e71e694e38788b15285854d21ed88eb54bda2ae5e7b7aa4e04d1",
    "cross_cats_sorted": [
      "math.CO",
      "q-fin.EC"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.GT",
    "submitted_at": "2015-05-15T01:16:21Z",
    "title_canon_sha256": "4f6d84fbdd5d5c4b3e69e4a85b58bb76b8f1fcebe5832fed4e6c18798e665039"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1505.05737",
    "kind": "arxiv",
    "version": 4
  }
}