{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:3SMTP223TNICDXDL4KNGDRPAAE","short_pith_number":"pith:3SMTP223","canonical_record":{"source":{"id":"1905.03797","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2019-05-09T18:00:54Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"6598dedca3a6546395495909fcd4070b6e9f9b8a295dd25fdc32b19fa9847f77","abstract_canon_sha256":"10e4d21a11285db6d0fcd0abc94611932dce583feb9f59d73455530ebd79c732"},"schema_version":"1.0"},"canonical_sha256":"dc9937eb5b9b5021dc6be29a61c5e0012d58c12c49675b3fba2c13aacf3ea179","source":{"kind":"arxiv","id":"1905.03797","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1905.03797","created_at":"2026-07-05T03:49:06Z"},{"alias_kind":"arxiv_version","alias_value":"1905.03797v3","created_at":"2026-07-05T03:49:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1905.03797","created_at":"2026-07-05T03:49:06Z"},{"alias_kind":"pith_short_12","alias_value":"3SMTP223TNIC","created_at":"2026-07-05T03:49:06Z"},{"alias_kind":"pith_short_16","alias_value":"3SMTP223TNICDXDL","created_at":"2026-07-05T03:49:06Z"},{"alias_kind":"pith_short_8","alias_value":"3SMTP223","created_at":"2026-07-05T03:49:06Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:3SMTP223TNICDXDL4KNGDRPAAE","target":"record","payload":{"canonical_record":{"source":{"id":"1905.03797","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2019-05-09T18:00:54Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"6598dedca3a6546395495909fcd4070b6e9f9b8a295dd25fdc32b19fa9847f77","abstract_canon_sha256":"10e4d21a11285db6d0fcd0abc94611932dce583feb9f59d73455530ebd79c732"},"schema_version":"1.0"},"canonical_sha256":"dc9937eb5b9b5021dc6be29a61c5e0012d58c12c49675b3fba2c13aacf3ea179","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T03:49:06.645906Z","signature_b64":"37ffVfk9VGF/5LjgP9+SSiGK79nYrwPeCPRK80iY4AKLpZjV1ZxNCkO4O/GCoo6bT9jfmGPD0YQI3YjArg/gCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"dc9937eb5b9b5021dc6be29a61c5e0012d58c12c49675b3fba2c13aacf3ea179","last_reissued_at":"2026-07-05T03:49:06.645411Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T03:49:06.645411Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1905.03797","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T03:49:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hz+Tmu1s2VRf356P3NAWtbdvGSH3X9MigMgtyNIn6ebX1EpPWDLL/DqL8BAHAGF1rmq6uRaZnjCZPky2KW4OAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T23:07:06.674482Z"},"content_sha256":"5c98c70de60085c6e27127b047d6e2ef861980872bd24603ea010b3d14d6ed40","schema_version":"1.0","event_id":"sha256:5c98c70de60085c6e27127b047d6e2ef861980872bd24603ea010b3d14d6ed40"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:3SMTP223TNICDXDL4KNGDRPAAE","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"$N_\\infty$-operads and associahedra","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.AT","authors_text":"Constanze Roitzheim, David Barnes, Scott Balchin","submitted_at":"2019-05-09T18:00:54Z","abstract_excerpt":"We provide a new combinatorial approach to studying the collection of N-infinity-operads in G-equivariant homotopy theory for G a finite cyclic group. In particular, we show that for G the cyclic group of order p^n the natural order on the collection of N-infinity-operads stands in bijection with the poset structure of the (n+1)-associahedron. We further provide a lower bound for the number of possible N-infinity-operads for any finite cyclic group G."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1905.03797","kind":"arxiv","version":3},"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/1905.03797/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":"2026-07-05T03:49:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FnRBy9J/eWVuSdYiV5dn2FXHdu2cpYtRd+3QQOWXkZYaG9u6kBqkECZ8oGuuGOF+o/bOHmcA+g+FGe51U1CCAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T23:07:06.675140Z"},"content_sha256":"bd98ceb2c6339af9a26bc5347916373593d45fe79ccb7643810faf392a3d154a","schema_version":"1.0","event_id":"sha256:bd98ceb2c6339af9a26bc5347916373593d45fe79ccb7643810faf392a3d154a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/3SMTP223TNICDXDL4KNGDRPAAE/bundle.json","state_url":"https://pith.science/pith/3SMTP223TNICDXDL4KNGDRPAAE/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/3SMTP223TNICDXDL4KNGDRPAAE/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":"2026-08-08T23:07:06Z","links":{"resolver":"https://pith.science/pith/3SMTP223TNICDXDL4KNGDRPAAE","bundle":"https://pith.science/pith/3SMTP223TNICDXDL4KNGDRPAAE/bundle.json","state":"https://pith.science/pith/3SMTP223TNICDXDL4KNGDRPAAE/state.json","well_known_bundle":"https://pith.science/.well-known/pith/3SMTP223TNICDXDL4KNGDRPAAE/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:3SMTP223TNICDXDL4KNGDRPAAE","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":"10e4d21a11285db6d0fcd0abc94611932dce583feb9f59d73455530ebd79c732","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2019-05-09T18:00:54Z","title_canon_sha256":"6598dedca3a6546395495909fcd4070b6e9f9b8a295dd25fdc32b19fa9847f77"},"schema_version":"1.0","source":{"id":"1905.03797","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1905.03797","created_at":"2026-07-05T03:49:06Z"},{"alias_kind":"arxiv_version","alias_value":"1905.03797v3","created_at":"2026-07-05T03:49:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1905.03797","created_at":"2026-07-05T03:49:06Z"},{"alias_kind":"pith_short_12","alias_value":"3SMTP223TNIC","created_at":"2026-07-05T03:49:06Z"},{"alias_kind":"pith_short_16","alias_value":"3SMTP223TNICDXDL","created_at":"2026-07-05T03:49:06Z"},{"alias_kind":"pith_short_8","alias_value":"3SMTP223","created_at":"2026-07-05T03:49:06Z"}],"graph_snapshots":[{"event_id":"sha256:bd98ceb2c6339af9a26bc5347916373593d45fe79ccb7643810faf392a3d154a","target":"graph","created_at":"2026-07-05T03:49:06Z","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/1905.03797/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We provide a new combinatorial approach to studying the collection of N-infinity-operads in G-equivariant homotopy theory for G a finite cyclic group. In particular, we show that for G the cyclic group of order p^n the natural order on the collection of N-infinity-operads stands in bijection with the poset structure of the (n+1)-associahedron. We further provide a lower bound for the number of possible N-infinity-operads for any finite cyclic group G.","authors_text":"Constanze Roitzheim, David Barnes, Scott Balchin","cross_cats":["math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2019-05-09T18:00:54Z","title":"$N_\\infty$-operads and associahedra"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1905.03797","kind":"arxiv","version":3},"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":"sha256:5c98c70de60085c6e27127b047d6e2ef861980872bd24603ea010b3d14d6ed40","target":"record","created_at":"2026-07-05T03:49:06Z","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":"10e4d21a11285db6d0fcd0abc94611932dce583feb9f59d73455530ebd79c732","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2019-05-09T18:00:54Z","title_canon_sha256":"6598dedca3a6546395495909fcd4070b6e9f9b8a295dd25fdc32b19fa9847f77"},"schema_version":"1.0","source":{"id":"1905.03797","kind":"arxiv","version":3}},"canonical_sha256":"dc9937eb5b9b5021dc6be29a61c5e0012d58c12c49675b3fba2c13aacf3ea179","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"dc9937eb5b9b5021dc6be29a61c5e0012d58c12c49675b3fba2c13aacf3ea179","first_computed_at":"2026-07-05T03:49:06.645411Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T03:49:06.645411Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"37ffVfk9VGF/5LjgP9+SSiGK79nYrwPeCPRK80iY4AKLpZjV1ZxNCkO4O/GCoo6bT9jfmGPD0YQI3YjArg/gCA==","signature_status":"signed_v1","signed_at":"2026-07-05T03:49:06.645906Z","signed_message":"canonical_sha256_bytes"},"source_id":"1905.03797","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5c98c70de60085c6e27127b047d6e2ef861980872bd24603ea010b3d14d6ed40","sha256:bd98ceb2c6339af9a26bc5347916373593d45fe79ccb7643810faf392a3d154a"],"state_sha256":"056dbcc1d922a05138b9cebf396249d00904d2f769b6aa8fe40b5088e28e4318"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2fyHxRhC/ZcZotsvweX9yuEcIOeGkImFDOVLCN22/IcfSDCTc5NKDDCaUZshypoSpvQGIrCkCQw5TTf9HKj7AA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-08T23:07:06.679050Z","bundle_sha256":"5188de3e758784d1beb20366abfc6d1051ecbafd853eea0da41bc294fa68e604"}}