Pith Number

pith:3DNZJIXE

pith:2023:3DNZJIXE2BK7UZFHQAODRUGQVN

not attested not anchored not stored refs pending

Irreducibility of Generalized Permutohedra, Supermodular Functions, and Balanced Multisets

Milan Haiman, Yuan Yao

arxiv:2303.05751 v1 · 2023-03-10 · math.CO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{3DNZJIXE2BK7UZFHQAODRUGQVN}

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	2026-07-05T05:49:47.197121Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d8db94a2e4d055fa64a7801c38d0d0ab585e95b9606a045595a050d81d89ca2b

Aliases

arxiv: 2303.05751 · arxiv_version: 2303.05751v1 · doi: 10.48550/arxiv.2303.05751 · pith_short_12: 3DNZJIXE2BK7 · pith_short_16: 3DNZJIXE2BK7UZFH · pith_short_8: 3DNZJIXE

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/3DNZJIXE2BK7UZFHQAODRUGQVN \
  | 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: d8db94a2e4d055fa64a7801c38d0d0ab585e95b9606a045595a050d81d89ca2b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "63fdd18b7cd06dda2b6878a3fc443110e678efab466009eaff6683fc180a60dc",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2023-03-10T07:25:32Z",
    "title_canon_sha256": "4a9e381df938519848914e2f7ca3d81226f2a85b4ca3c314cebcdec13470f38b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2303.05751",
    "kind": "arxiv",
    "version": 1
  }
}