Pith Number

pith:4PXW5UZL

pith:2021:4PXW5UZLRLELJO5DUBFH4XXLYC

not attested not anchored not stored refs pending

Optimal Vaccine Allocation for Pandemic Stabilization

Alex Olshevsky, Qianqian Ma, Yang-Yu Liu

arxiv:2109.04612 v1 · 2021-09-10 · math.OC · q-bio.PE

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{4PXW5UZLRLELJO5DUBFH4XXLYC}

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	2026-07-05T03:13:07.817879Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e3ef6ed32b8ac8b4bba3a04a7e5eebc0a0a457a36273acb8066e1b7c9cfd5f02

Aliases

arxiv: 2109.04612 · arxiv_version: 2109.04612v1 · doi: 10.48550/arxiv.2109.04612 · pith_short_12: 4PXW5UZLRLEL · pith_short_16: 4PXW5UZLRLELJO5D · pith_short_8: 4PXW5UZL

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/4PXW5UZLRLELJO5DUBFH4XXLYC \
  | 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: e3ef6ed32b8ac8b4bba3a04a7e5eebc0a0a457a36273acb8066e1b7c9cfd5f02

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "14fead729470088724513a33f97031eaddda7c629330ac1f43da70ab7296f800",
    "cross_cats_sorted": [
      "q-bio.PE"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OC",
    "submitted_at": "2021-09-10T01:50:47Z",
    "title_canon_sha256": "69a4f15fd6d171c522ab04abe548aabf18f13a96adf56db9f3fbba2f38f3e098"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2109.04612",
    "kind": "arxiv",
    "version": 1
  }
}