{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:H6CD6PLGJLRZ7A7YOQVINVHUZD","short_pith_number":"pith:H6CD6PLG","canonical_record":{"source":{"id":"1705.04024","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2017-05-11T06:08:37Z","cross_cats_sorted":[],"title_canon_sha256":"881271ff8939827dab8c28157dcab99db3e94f0181ec286d349d0724c6673bd7","abstract_canon_sha256":"e94098e0fcd48dd961972faf0dede878edfd47870eb9137c32d52ee4974b6d37"},"schema_version":"1.0"},"canonical_sha256":"3f843f3d664ae39f83f8742a86d4f4c8fb991e927488b6278bf4b3a64186bec8","source":{"kind":"arxiv","id":"1705.04024","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1705.04024","created_at":"2026-05-18T00:44:41Z"},{"alias_kind":"arxiv_version","alias_value":"1705.04024v1","created_at":"2026-05-18T00:44:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.04024","created_at":"2026-05-18T00:44:41Z"},{"alias_kind":"pith_short_12","alias_value":"H6CD6PLGJLRZ","created_at":"2026-05-18T12:31:18Z"},{"alias_kind":"pith_short_16","alias_value":"H6CD6PLGJLRZ7A7Y","created_at":"2026-05-18T12:31:18Z"},{"alias_kind":"pith_short_8","alias_value":"H6CD6PLG","created_at":"2026-05-18T12:31:18Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:H6CD6PLGJLRZ7A7YOQVINVHUZD","target":"record","payload":{"canonical_record":{"source":{"id":"1705.04024","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2017-05-11T06:08:37Z","cross_cats_sorted":[],"title_canon_sha256":"881271ff8939827dab8c28157dcab99db3e94f0181ec286d349d0724c6673bd7","abstract_canon_sha256":"e94098e0fcd48dd961972faf0dede878edfd47870eb9137c32d52ee4974b6d37"},"schema_version":"1.0"},"canonical_sha256":"3f843f3d664ae39f83f8742a86d4f4c8fb991e927488b6278bf4b3a64186bec8","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:44:41.594001Z","signature_b64":"j7NxASk1Si4DgVg0BcXc6bgZJGn6DSnHkldHksbQL3UvAnKDoC2BJkOhkD4vYgdZyedCRWEUQu2fFCvrVajYCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3f843f3d664ae39f83f8742a86d4f4c8fb991e927488b6278bf4b3a64186bec8","last_reissued_at":"2026-05-18T00:44:41.593392Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:44:41.593392Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1705.04024","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":"2026-05-18T00:44:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LdntCTqaHkQ8BHJV1kGEA1nQZHXO+KsgAvY3/evCwqpNLE3RWNAbww+ejezWHm/1N6+tgLCVafAH7SChHQi1AA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T01:40:33.134459Z"},"content_sha256":"bf3f85f957ecbcc434f8bbdbda834e7dbbcd3149a2ec19e05f338737bdbc7305","schema_version":"1.0","event_id":"sha256:bf3f85f957ecbcc434f8bbdbda834e7dbbcd3149a2ec19e05f338737bdbc7305"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:H6CD6PLGJLRZ7A7YOQVINVHUZD","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On Regular Sequences in the Form Module with Applications to Local B\\'ezout Inequalities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"M. Azeem Khadam","submitted_at":"2017-05-11T06:08:37Z","abstract_excerpt":"Let $\\mathfrak{q}$ denote an ideal in a Noetherian local ring $(A,\\mathfrak{m})$. Let $\\underline{a}=a_1,\\ldots,a_d \\subset \\mathfrak{q}$ denote a system of parameters in a finitely generated $A$-module $M$. This note investigate an improvement of the inequality $c_1\\cdot \\ldots \\cdot c_d \\cdot e_0(\\mathfrak{q};M) \\leq \\ell_A(M/\\underline{a}\\,M)$, where $c_i$ denote the initial degrees of $a_i$ in the form ring $G_A(\\mathfrak{q})$. To this end, there is an investigation of regular sequences in the form module $G_M(\\mathfrak{q})$ by homology of a factor complex of the Koszul complex. In a parti"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.04024","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":"2026-05-18T00:44:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"h1NW4Co6UfukJITzJlx0B5ySKeTkeaScCs9+5diYOQMl8vDE/8ePczsQaRZmcmHA40Io1u1LcGw/PHq2iFYuAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T01:40:33.135186Z"},"content_sha256":"ad74d5f6c9a56da4673b5d243cf2cb65a474010de0b51aee1a505856adb2e795","schema_version":"1.0","event_id":"sha256:ad74d5f6c9a56da4673b5d243cf2cb65a474010de0b51aee1a505856adb2e795"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/H6CD6PLGJLRZ7A7YOQVINVHUZD/bundle.json","state_url":"https://pith.science/pith/H6CD6PLGJLRZ7A7YOQVINVHUZD/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/H6CD6PLGJLRZ7A7YOQVINVHUZD/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":"2026-06-08T01:40:33Z","links":{"resolver":"https://pith.science/pith/H6CD6PLGJLRZ7A7YOQVINVHUZD","bundle":"https://pith.science/pith/H6CD6PLGJLRZ7A7YOQVINVHUZD/bundle.json","state":"https://pith.science/pith/H6CD6PLGJLRZ7A7YOQVINVHUZD/state.json","well_known_bundle":"https://pith.science/.well-known/pith/H6CD6PLGJLRZ7A7YOQVINVHUZD/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:H6CD6PLGJLRZ7A7YOQVINVHUZD","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":"e94098e0fcd48dd961972faf0dede878edfd47870eb9137c32d52ee4974b6d37","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2017-05-11T06:08:37Z","title_canon_sha256":"881271ff8939827dab8c28157dcab99db3e94f0181ec286d349d0724c6673bd7"},"schema_version":"1.0","source":{"id":"1705.04024","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1705.04024","created_at":"2026-05-18T00:44:41Z"},{"alias_kind":"arxiv_version","alias_value":"1705.04024v1","created_at":"2026-05-18T00:44:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.04024","created_at":"2026-05-18T00:44:41Z"},{"alias_kind":"pith_short_12","alias_value":"H6CD6PLGJLRZ","created_at":"2026-05-18T12:31:18Z"},{"alias_kind":"pith_short_16","alias_value":"H6CD6PLGJLRZ7A7Y","created_at":"2026-05-18T12:31:18Z"},{"alias_kind":"pith_short_8","alias_value":"H6CD6PLG","created_at":"2026-05-18T12:31:18Z"}],"graph_snapshots":[{"event_id":"sha256:ad74d5f6c9a56da4673b5d243cf2cb65a474010de0b51aee1a505856adb2e795","target":"graph","created_at":"2026-05-18T00:44:41Z","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":"Let $\\mathfrak{q}$ denote an ideal in a Noetherian local ring $(A,\\mathfrak{m})$. Let $\\underline{a}=a_1,\\ldots,a_d \\subset \\mathfrak{q}$ denote a system of parameters in a finitely generated $A$-module $M$. This note investigate an improvement of the inequality $c_1\\cdot \\ldots \\cdot c_d \\cdot e_0(\\mathfrak{q};M) \\leq \\ell_A(M/\\underline{a}\\,M)$, where $c_i$ denote the initial degrees of $a_i$ in the form ring $G_A(\\mathfrak{q})$. To this end, there is an investigation of regular sequences in the form module $G_M(\\mathfrak{q})$ by homology of a factor complex of the Koszul complex. In a parti","authors_text":"M. Azeem Khadam","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2017-05-11T06:08:37Z","title":"On Regular Sequences in the Form Module with Applications to Local B\\'ezout Inequalities"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.04024","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:bf3f85f957ecbcc434f8bbdbda834e7dbbcd3149a2ec19e05f338737bdbc7305","target":"record","created_at":"2026-05-18T00:44:41Z","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":"e94098e0fcd48dd961972faf0dede878edfd47870eb9137c32d52ee4974b6d37","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2017-05-11T06:08:37Z","title_canon_sha256":"881271ff8939827dab8c28157dcab99db3e94f0181ec286d349d0724c6673bd7"},"schema_version":"1.0","source":{"id":"1705.04024","kind":"arxiv","version":1}},"canonical_sha256":"3f843f3d664ae39f83f8742a86d4f4c8fb991e927488b6278bf4b3a64186bec8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3f843f3d664ae39f83f8742a86d4f4c8fb991e927488b6278bf4b3a64186bec8","first_computed_at":"2026-05-18T00:44:41.593392Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:44:41.593392Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"j7NxASk1Si4DgVg0BcXc6bgZJGn6DSnHkldHksbQL3UvAnKDoC2BJkOhkD4vYgdZyedCRWEUQu2fFCvrVajYCw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:44:41.594001Z","signed_message":"canonical_sha256_bytes"},"source_id":"1705.04024","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bf3f85f957ecbcc434f8bbdbda834e7dbbcd3149a2ec19e05f338737bdbc7305","sha256:ad74d5f6c9a56da4673b5d243cf2cb65a474010de0b51aee1a505856adb2e795"],"state_sha256":"e370922ae5646a4f5eacb7c6fe728bbe62dc138d71e95762694c77104c8991db"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Uku4hGBThp+vlJ8EupOK25JtGlzRzGZdQK6OTMMd5k065Cnr0P6JNBKeH1bwZO8JMAYuw+eQHPOnAcjLbnjQBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-08T01:40:33.138849Z","bundle_sha256":"45fa943c0daf5b99a0187774c7c53f01c85ebdbf374f821de6f15aa57e58710c"}}