Pith Number

pith:K7PCG53E

pith:2016:K7PCG53E2V2EOTALGOBWY75P5G

not attested not anchored not stored refs pending

Optimal Control of a Tuberculosis Model with State and Control Delays

Cristiana J. Silva, Delfim F. M. Torres, Helmut Maurer

arxiv:1606.08721 v1 · 2016-06-28 · 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{K7PCG53E2V2EOTALGOBWY75P5G}

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	2026-05-18T01:03:05.897114Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

57de237764d574474c0b33836c7fafe9bdda701e8f4b47aa65444e982b079c5d

Aliases

arxiv: 1606.08721 · arxiv_version: 1606.08721v1 · doi: 10.48550/arxiv.1606.08721 · pith_short_12: K7PCG53E2V2E · pith_short_16: K7PCG53E2V2EOTAL · pith_short_8: K7PCG53E

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/K7PCG53E2V2EOTALGOBWY75P5G \
  | 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: 57de237764d574474c0b33836c7fafe9bdda701e8f4b47aa65444e982b079c5d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3e05d08f9aa7b2f46016776688413bc31a1bea74ba212c4cc1a73116a6c60fdb",
    "cross_cats_sorted": [
      "q-bio.PE"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OC",
    "submitted_at": "2016-06-28T14:23:29Z",
    "title_canon_sha256": "6d091078d957667a5fc74c035eae748c8642ee2481723bdc72e04dbf707de2dc"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1606.08721",
    "kind": "arxiv",
    "version": 1
  }
}