{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2021:PKAZUTN5LKS7CHSRY6L3Z2EWBW","short_pith_number":"pith:PKAZUTN5","canonical_record":{"source":{"id":"2106.10320","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2021-06-18T19:20:34Z","cross_cats_sorted":[],"title_canon_sha256":"9a0ac323f10b3ac72d69785d180fa310c67153f8cde6c5100a79a39bf354eb6d","abstract_canon_sha256":"a42ab7f9277e90685adbf893b9848a62275a66fa4ebfab7335489e3d884aa93c"},"schema_version":"1.0"},"canonical_sha256":"7a819a4dbd5aa5f11e51c797bce8960db0fb99b399fd07064cd11bd784f55531","source":{"kind":"arxiv","id":"2106.10320","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2106.10320","created_at":"2026-07-05T03:54:00Z"},{"alias_kind":"arxiv_version","alias_value":"2106.10320v2","created_at":"2026-07-05T03:54:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2106.10320","created_at":"2026-07-05T03:54:00Z"},{"alias_kind":"pith_short_12","alias_value":"PKAZUTN5LKS7","created_at":"2026-07-05T03:54:00Z"},{"alias_kind":"pith_short_16","alias_value":"PKAZUTN5LKS7CHSR","created_at":"2026-07-05T03:54:00Z"},{"alias_kind":"pith_short_8","alias_value":"PKAZUTN5","created_at":"2026-07-05T03:54:00Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2021:PKAZUTN5LKS7CHSRY6L3Z2EWBW","target":"record","payload":{"canonical_record":{"source":{"id":"2106.10320","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2021-06-18T19:20:34Z","cross_cats_sorted":[],"title_canon_sha256":"9a0ac323f10b3ac72d69785d180fa310c67153f8cde6c5100a79a39bf354eb6d","abstract_canon_sha256":"a42ab7f9277e90685adbf893b9848a62275a66fa4ebfab7335489e3d884aa93c"},"schema_version":"1.0"},"canonical_sha256":"7a819a4dbd5aa5f11e51c797bce8960db0fb99b399fd07064cd11bd784f55531","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T03:54:00.905915Z","signature_b64":"6lL3apcbdKxDlT9ybNA/9b2cA16CnDIb54ts5y6hZk50FeB8Biz32dvk6WzfbigfZGovUVZSg0lUZxsqdk6sDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7a819a4dbd5aa5f11e51c797bce8960db0fb99b399fd07064cd11bd784f55531","last_reissued_at":"2026-07-05T03:54:00.905436Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T03:54:00.905436Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2106.10320","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T03:54:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7U4Je5WKZjZrqNEHznwzw7pgfyqm5FL+ZZRmMkeRL/DnRhNUJNhcVjMSDZQtuI1JDXvgSxt71gEKaClHAoQ2Cg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-23T18:18:37.173915Z"},"content_sha256":"87a2d56b80fe123e9624c64756b9b23d7e44347d63dccef96f6939418272dd2e","schema_version":"1.0","event_id":"sha256:87a2d56b80fe123e9624c64756b9b23d7e44347d63dccef96f6939418272dd2e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2021:PKAZUTN5LKS7CHSRY6L3Z2EWBW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Asymptotic distribution of odd-balanced unimodal sequences with rank congruent to a mod c","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Taylor Garnowski","submitted_at":"2021-06-18T19:20:34Z","abstract_excerpt":"We compute an asymptotic estimate for odd balanced unimodal sequences for ranks congruent to $a \\pmod{c}$ for $c\\neq 1$ odd. We find the interesting result that the odd balanced unimodal sequences are asymptotically related to the overpartition function. This is in contrast to strongly unimodal sequences which, are asymptotically related to the partition function."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2106.10320","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2106.10320/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T03:54:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"oM3Sl6Bq7/Qa3dD7q5jT88pbbn4BL1zEVco+L8CWHFlYDshhTneqOf3Trp/XjjmZItYIW0R24olvQY9pMlt1Cg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-23T18:18:37.174392Z"},"content_sha256":"f0dcd9c863d618adab4237e0629000b3645930c672fe9a92f8afe5884075464f","schema_version":"1.0","event_id":"sha256:f0dcd9c863d618adab4237e0629000b3645930c672fe9a92f8afe5884075464f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/PKAZUTN5LKS7CHSRY6L3Z2EWBW/bundle.json","state_url":"https://pith.science/pith/PKAZUTN5LKS7CHSRY6L3Z2EWBW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/PKAZUTN5LKS7CHSRY6L3Z2EWBW/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-08-23T18:18:37Z","links":{"resolver":"https://pith.science/pith/PKAZUTN5LKS7CHSRY6L3Z2EWBW","bundle":"https://pith.science/pith/PKAZUTN5LKS7CHSRY6L3Z2EWBW/bundle.json","state":"https://pith.science/pith/PKAZUTN5LKS7CHSRY6L3Z2EWBW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/PKAZUTN5LKS7CHSRY6L3Z2EWBW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:PKAZUTN5LKS7CHSRY6L3Z2EWBW","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"a42ab7f9277e90685adbf893b9848a62275a66fa4ebfab7335489e3d884aa93c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2021-06-18T19:20:34Z","title_canon_sha256":"9a0ac323f10b3ac72d69785d180fa310c67153f8cde6c5100a79a39bf354eb6d"},"schema_version":"1.0","source":{"id":"2106.10320","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2106.10320","created_at":"2026-07-05T03:54:00Z"},{"alias_kind":"arxiv_version","alias_value":"2106.10320v2","created_at":"2026-07-05T03:54:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2106.10320","created_at":"2026-07-05T03:54:00Z"},{"alias_kind":"pith_short_12","alias_value":"PKAZUTN5LKS7","created_at":"2026-07-05T03:54:00Z"},{"alias_kind":"pith_short_16","alias_value":"PKAZUTN5LKS7CHSR","created_at":"2026-07-05T03:54:00Z"},{"alias_kind":"pith_short_8","alias_value":"PKAZUTN5","created_at":"2026-07-05T03:54:00Z"}],"graph_snapshots":[{"event_id":"sha256:f0dcd9c863d618adab4237e0629000b3645930c672fe9a92f8afe5884075464f","target":"graph","created_at":"2026-07-05T03:54:00Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2106.10320/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We compute an asymptotic estimate for odd balanced unimodal sequences for ranks congruent to $a \\pmod{c}$ for $c\\neq 1$ odd. We find the interesting result that the odd balanced unimodal sequences are asymptotically related to the overpartition function. This is in contrast to strongly unimodal sequences which, are asymptotically related to the partition function.","authors_text":"Taylor Garnowski","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2021-06-18T19:20:34Z","title":"Asymptotic distribution of odd-balanced unimodal sequences with rank congruent to a mod c"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2106.10320","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:87a2d56b80fe123e9624c64756b9b23d7e44347d63dccef96f6939418272dd2e","target":"record","created_at":"2026-07-05T03:54:00Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"a42ab7f9277e90685adbf893b9848a62275a66fa4ebfab7335489e3d884aa93c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2021-06-18T19:20:34Z","title_canon_sha256":"9a0ac323f10b3ac72d69785d180fa310c67153f8cde6c5100a79a39bf354eb6d"},"schema_version":"1.0","source":{"id":"2106.10320","kind":"arxiv","version":2}},"canonical_sha256":"7a819a4dbd5aa5f11e51c797bce8960db0fb99b399fd07064cd11bd784f55531","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7a819a4dbd5aa5f11e51c797bce8960db0fb99b399fd07064cd11bd784f55531","first_computed_at":"2026-07-05T03:54:00.905436Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T03:54:00.905436Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"6lL3apcbdKxDlT9ybNA/9b2cA16CnDIb54ts5y6hZk50FeB8Biz32dvk6WzfbigfZGovUVZSg0lUZxsqdk6sDg==","signature_status":"signed_v1","signed_at":"2026-07-05T03:54:00.905915Z","signed_message":"canonical_sha256_bytes"},"source_id":"2106.10320","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:87a2d56b80fe123e9624c64756b9b23d7e44347d63dccef96f6939418272dd2e","sha256:f0dcd9c863d618adab4237e0629000b3645930c672fe9a92f8afe5884075464f"],"state_sha256":"ad9ebb95f1eb38f93f8521020746508b35c86e314da431e73eb45cc87fd1f819"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9HMAfX8x/D9LfmJ4jf/Q9J0Ql1gIHXW+7JwMTKn4ksDOAMttiCkNUXfAFbrE3fhhCCkCB1QvDElL3wyDl1aADg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-23T18:18:37.179146Z","bundle_sha256":"82fdaf731355ac871243b2f343b721b32a689ba971f047ed4bb36e58bcb0f039"}}