Pith Number

pith:GYPJJB6M

pith:2026:GYPJJB6MYD2DMP6KVJ5TUNJPF5

not attested not anchored not stored refs pending

Positivity and tails of Jacobi theta series

Nian Hong Zhou

arxiv:2607.10968 v1 · 2026-07-13 · math.NT · 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{GYPJJB6MYD2DMP6KVJ5TUNJPF5}

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	2026-07-14T01:21:49.989816Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

361e9487ccc0f4363fcaaa7b3a352f2f64a28e9a9c9a7dd438356866fa698b0d

Aliases

arxiv: 2607.10968 · arxiv_version: 2607.10968v1 · doi: 10.48550/arxiv.2607.10968 · pith_short_12: GYPJJB6MYD2D · pith_short_16: GYPJJB6MYD2DMP6K · pith_short_8: GYPJJB6M

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/GYPJJB6MYD2DMP6KVJ5TUNJPF5 \
  | 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: 361e9487ccc0f4363fcaaa7b3a352f2f64a28e9a9c9a7dd438356866fa698b0d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "17cc80df62166ad050b85fb555405e4866e541c96345f1f432698db268c80f8d",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2026-07-13T00:26:41Z",
    "title_canon_sha256": "e4fe5a28acbcc3ebc6865a2101def30f990e690a98f4957fd4469c3f75e52577"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.10968",
    "kind": "arxiv",
    "version": 1
  }
}