{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:JQ6CDWJ7LY24E5LZ7ZSZVV5RY6","short_pith_number":"pith:JQ6CDWJ7","canonical_record":{"source":{"id":"1407.0154","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-07-01T09:30:03Z","cross_cats_sorted":[],"title_canon_sha256":"2a983a673d7732313e8a54f6c5f54655743a2f84d825b6d0c9c2e93ffbb7b8ea","abstract_canon_sha256":"9eff6343083f820b649331b7f524020d59cd1da763bd6a8db9cd02bd6e183a13"},"schema_version":"1.0"},"canonical_sha256":"4c3c21d93f5e35c27579fe659ad7b1c7bec3db2d411fe80d65a4aa6bce787ca8","source":{"kind":"arxiv","id":"1407.0154","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1407.0154","created_at":"2026-05-18T02:48:35Z"},{"alias_kind":"arxiv_version","alias_value":"1407.0154v1","created_at":"2026-05-18T02:48:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1407.0154","created_at":"2026-05-18T02:48:35Z"},{"alias_kind":"pith_short_12","alias_value":"JQ6CDWJ7LY24","created_at":"2026-05-18T12:28:35Z"},{"alias_kind":"pith_short_16","alias_value":"JQ6CDWJ7LY24E5LZ","created_at":"2026-05-18T12:28:35Z"},{"alias_kind":"pith_short_8","alias_value":"JQ6CDWJ7","created_at":"2026-05-18T12:28:35Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:JQ6CDWJ7LY24E5LZ7ZSZVV5RY6","target":"record","payload":{"canonical_record":{"source":{"id":"1407.0154","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-07-01T09:30:03Z","cross_cats_sorted":[],"title_canon_sha256":"2a983a673d7732313e8a54f6c5f54655743a2f84d825b6d0c9c2e93ffbb7b8ea","abstract_canon_sha256":"9eff6343083f820b649331b7f524020d59cd1da763bd6a8db9cd02bd6e183a13"},"schema_version":"1.0"},"canonical_sha256":"4c3c21d93f5e35c27579fe659ad7b1c7bec3db2d411fe80d65a4aa6bce787ca8","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:48:35.020160Z","signature_b64":"ZgxaRK134+LNvf1aPqXFtpaBDk4vDPq272H60k64gbIB9nl9oRDOcqi8Y4NsOmxw6WCQPNH1KA5eV4JtyClQCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4c3c21d93f5e35c27579fe659ad7b1c7bec3db2d411fe80d65a4aa6bce787ca8","last_reissued_at":"2026-05-18T02:48:35.019432Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:48:35.019432Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1407.0154","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:48:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"w0P1NUQPr5MYXWkoyVut8zmwhIisdi4bvSLxrrSiCs3JgzqugIEi5Gy2tc/Qeyt0u+Bl9AoOP17Djgc+SeYvAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T16:19:44.089372Z"},"content_sha256":"ec31447a766ce0050867fdb4c89e83eb13599b44daa879cc50e3db416ef107fb","schema_version":"1.0","event_id":"sha256:ec31447a766ce0050867fdb4c89e83eb13599b44daa879cc50e3db416ef107fb"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:JQ6CDWJ7LY24E5LZ7ZSZVV5RY6","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Orbifold zeta functions for dual invertible polynomials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Sabir M.~Gusein-Zade, Wolfgang Ebeling","submitted_at":"2014-07-01T09:30:03Z","abstract_excerpt":"An invertible polynomial in $n$ variables is a quasihomogeneous polynomial consisting of $n$ monomials so that the weights of the variables and the quasi-degree are well defined. In the framework of the construction of mirror symmetric orbifold Landau--Ginzburg models, P.~Berg\\-lund, T.~H\\\"ubsch and M.~Henningson considered a pair $(f,G)$ consisting of an invertible polynomial $f$ and an abelian group $G$ of its symmetries together with a dual pair $(\\widetilde{f}, \\widetilde{G})$. Here we study the reduced orbifold zeta functions of dual pairs $(f,G)$ and $(\\widetilde{f}, \\widetilde{G})$ and "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.0154","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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":"2026-05-18T02:48:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"25FAMDYECMM7TU8X3YNB36vX+KkMcJob5nGA9J4qUKRqNjSvEKwBqYoG9gIXiH3Ijr9kN/fT14OILMytwlWFBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T16:19:44.089726Z"},"content_sha256":"f7ef75e35c2bb583ba031f2ccfc3d82ad526245c9bd781e50f4493a6acc050ee","schema_version":"1.0","event_id":"sha256:f7ef75e35c2bb583ba031f2ccfc3d82ad526245c9bd781e50f4493a6acc050ee"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/JQ6CDWJ7LY24E5LZ7ZSZVV5RY6/bundle.json","state_url":"https://pith.science/pith/JQ6CDWJ7LY24E5LZ7ZSZVV5RY6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/JQ6CDWJ7LY24E5LZ7ZSZVV5RY6/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":"2026-06-26T16:19:44Z","links":{"resolver":"https://pith.science/pith/JQ6CDWJ7LY24E5LZ7ZSZVV5RY6","bundle":"https://pith.science/pith/JQ6CDWJ7LY24E5LZ7ZSZVV5RY6/bundle.json","state":"https://pith.science/pith/JQ6CDWJ7LY24E5LZ7ZSZVV5RY6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/JQ6CDWJ7LY24E5LZ7ZSZVV5RY6/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:JQ6CDWJ7LY24E5LZ7ZSZVV5RY6","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":"9eff6343083f820b649331b7f524020d59cd1da763bd6a8db9cd02bd6e183a13","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-07-01T09:30:03Z","title_canon_sha256":"2a983a673d7732313e8a54f6c5f54655743a2f84d825b6d0c9c2e93ffbb7b8ea"},"schema_version":"1.0","source":{"id":"1407.0154","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1407.0154","created_at":"2026-05-18T02:48:35Z"},{"alias_kind":"arxiv_version","alias_value":"1407.0154v1","created_at":"2026-05-18T02:48:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1407.0154","created_at":"2026-05-18T02:48:35Z"},{"alias_kind":"pith_short_12","alias_value":"JQ6CDWJ7LY24","created_at":"2026-05-18T12:28:35Z"},{"alias_kind":"pith_short_16","alias_value":"JQ6CDWJ7LY24E5LZ","created_at":"2026-05-18T12:28:35Z"},{"alias_kind":"pith_short_8","alias_value":"JQ6CDWJ7","created_at":"2026-05-18T12:28:35Z"}],"graph_snapshots":[{"event_id":"sha256:f7ef75e35c2bb583ba031f2ccfc3d82ad526245c9bd781e50f4493a6acc050ee","target":"graph","created_at":"2026-05-18T02:48:35Z","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"},"paper":{"abstract_excerpt":"An invertible polynomial in $n$ variables is a quasihomogeneous polynomial consisting of $n$ monomials so that the weights of the variables and the quasi-degree are well defined. In the framework of the construction of mirror symmetric orbifold Landau--Ginzburg models, P.~Berg\\-lund, T.~H\\\"ubsch and M.~Henningson considered a pair $(f,G)$ consisting of an invertible polynomial $f$ and an abelian group $G$ of its symmetries together with a dual pair $(\\widetilde{f}, \\widetilde{G})$. Here we study the reduced orbifold zeta functions of dual pairs $(f,G)$ and $(\\widetilde{f}, \\widetilde{G})$ and ","authors_text":"Sabir M.~Gusein-Zade, Wolfgang Ebeling","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-07-01T09:30:03Z","title":"Orbifold zeta functions for dual invertible polynomials"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.0154","kind":"arxiv","version":1},"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:ec31447a766ce0050867fdb4c89e83eb13599b44daa879cc50e3db416ef107fb","target":"record","created_at":"2026-05-18T02:48:35Z","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":"9eff6343083f820b649331b7f524020d59cd1da763bd6a8db9cd02bd6e183a13","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-07-01T09:30:03Z","title_canon_sha256":"2a983a673d7732313e8a54f6c5f54655743a2f84d825b6d0c9c2e93ffbb7b8ea"},"schema_version":"1.0","source":{"id":"1407.0154","kind":"arxiv","version":1}},"canonical_sha256":"4c3c21d93f5e35c27579fe659ad7b1c7bec3db2d411fe80d65a4aa6bce787ca8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4c3c21d93f5e35c27579fe659ad7b1c7bec3db2d411fe80d65a4aa6bce787ca8","first_computed_at":"2026-05-18T02:48:35.019432Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:48:35.019432Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ZgxaRK134+LNvf1aPqXFtpaBDk4vDPq272H60k64gbIB9nl9oRDOcqi8Y4NsOmxw6WCQPNH1KA5eV4JtyClQCw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:48:35.020160Z","signed_message":"canonical_sha256_bytes"},"source_id":"1407.0154","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ec31447a766ce0050867fdb4c89e83eb13599b44daa879cc50e3db416ef107fb","sha256:f7ef75e35c2bb583ba031f2ccfc3d82ad526245c9bd781e50f4493a6acc050ee"],"state_sha256":"7e31de6bf3f28c0a78f848a6a54daca608418228cb20327223d013856badc5da"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dj7Yl0cdU8qW/QDRkTKaDFvsgAh/PJl29cjMcan33WC0WsLH2pCHWIb4ldj++OMDQ+BCYBXorFXZrmvM/uzNCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-26T16:19:44.091729Z","bundle_sha256":"f11e2b17c98e525957488201266adbb5ff599a04a3d8701e1e79f321a9a4b170"}}