{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:HYHDGH4IEM35OILWKKPRITHD7T","short_pith_number":"pith:HYHDGH4I","canonical_record":{"source":{"id":"1711.11149","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2017-11-29T23:24:57Z","cross_cats_sorted":[],"title_canon_sha256":"5c4cf05b699e15905cbcac86fd4d3b3ffd3f2c786e6746cc64508cea82e2170f","abstract_canon_sha256":"5f11bd70872eee8ce33bd1c6341162633896ddb802a4b075c632d96d62e25b69"},"schema_version":"1.0"},"canonical_sha256":"3e0e331f882337d72176529f144ce3fcfea1c3ce57b88344a109cd9c0ca57a61","source":{"kind":"arxiv","id":"1711.11149","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1711.11149","created_at":"2026-05-17T23:42:14Z"},{"alias_kind":"arxiv_version","alias_value":"1711.11149v2","created_at":"2026-05-17T23:42:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1711.11149","created_at":"2026-05-17T23:42:14Z"},{"alias_kind":"pith_short_12","alias_value":"HYHDGH4IEM35","created_at":"2026-05-18T12:31:21Z"},{"alias_kind":"pith_short_16","alias_value":"HYHDGH4IEM35OILW","created_at":"2026-05-18T12:31:21Z"},{"alias_kind":"pith_short_8","alias_value":"HYHDGH4I","created_at":"2026-05-18T12:31:21Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:HYHDGH4IEM35OILWKKPRITHD7T","target":"record","payload":{"canonical_record":{"source":{"id":"1711.11149","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2017-11-29T23:24:57Z","cross_cats_sorted":[],"title_canon_sha256":"5c4cf05b699e15905cbcac86fd4d3b3ffd3f2c786e6746cc64508cea82e2170f","abstract_canon_sha256":"5f11bd70872eee8ce33bd1c6341162633896ddb802a4b075c632d96d62e25b69"},"schema_version":"1.0"},"canonical_sha256":"3e0e331f882337d72176529f144ce3fcfea1c3ce57b88344a109cd9c0ca57a61","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:42:14.294572Z","signature_b64":"x5dp5RcqfyKcuOP1QjCZN6okP5Ekrny+3YKCqcjlygftNUMXceHblYcyiGCNfXxkezFeYUkCMcrAnrly6N6KCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3e0e331f882337d72176529f144ce3fcfea1c3ce57b88344a109cd9c0ca57a61","last_reissued_at":"2026-05-17T23:42:14.293830Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:42:14.293830Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1711.11149","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":"2026-05-17T23:42:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LYOZQ/yH1YKrp4e2vtRd5tl7q08reve34ZZ3GPLti3lxjZzb2pHcAZ09CuM4YBWnLCBYWRx4qXFfzH865dKVAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T19:22:38.949710Z"},"content_sha256":"da33608da1c63bb589eda3267c142cbea1708855ac011ff9e0278f5cec05ce7f","schema_version":"1.0","event_id":"sha256:da33608da1c63bb589eda3267c142cbea1708855ac011ff9e0278f5cec05ce7f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:HYHDGH4IEM35OILWKKPRITHD7T","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the multiplicity of tangent cones of monomial curves","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Alessio Sammartano","submitted_at":"2017-11-29T23:24:57Z","abstract_excerpt":"Let $\\Lambda$ be a numerical semigroup, $\\mathcal{C}\\subseteq \\mathbb{A}^n$ the monomial curve singularity associated to $\\Lambda$, and $\\mathcal{T}$ its tangent cone. In this paper we provide a sharp upper bound for the least positive integer in $\\Lambda$ in terms of the codimension and the maximum degree of the equations of $\\mathcal{T}$, when $\\mathcal{T}$ is not a complete intersection. A special case of this result settles a question of J. Herzog and D. Stamate."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.11149","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":""},"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":"2026-05-17T23:42:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rneFIQryV4BdXeafQ059hbQugJnIrrMWSg4JrK+bPolMwSyass3h46VgaEb4axfKAlEnIoKOQeN/R4vvW0yQBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T19:22:38.950140Z"},"content_sha256":"0c938bb6fe495ed3e93c4d2bf300e04dd153815f5f1f2556daa600ede7a89c66","schema_version":"1.0","event_id":"sha256:0c938bb6fe495ed3e93c4d2bf300e04dd153815f5f1f2556daa600ede7a89c66"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/HYHDGH4IEM35OILWKKPRITHD7T/bundle.json","state_url":"https://pith.science/pith/HYHDGH4IEM35OILWKKPRITHD7T/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/HYHDGH4IEM35OILWKKPRITHD7T/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":"2026-05-31T19:22:38Z","links":{"resolver":"https://pith.science/pith/HYHDGH4IEM35OILWKKPRITHD7T","bundle":"https://pith.science/pith/HYHDGH4IEM35OILWKKPRITHD7T/bundle.json","state":"https://pith.science/pith/HYHDGH4IEM35OILWKKPRITHD7T/state.json","well_known_bundle":"https://pith.science/.well-known/pith/HYHDGH4IEM35OILWKKPRITHD7T/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:HYHDGH4IEM35OILWKKPRITHD7T","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":"5f11bd70872eee8ce33bd1c6341162633896ddb802a4b075c632d96d62e25b69","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2017-11-29T23:24:57Z","title_canon_sha256":"5c4cf05b699e15905cbcac86fd4d3b3ffd3f2c786e6746cc64508cea82e2170f"},"schema_version":"1.0","source":{"id":"1711.11149","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1711.11149","created_at":"2026-05-17T23:42:14Z"},{"alias_kind":"arxiv_version","alias_value":"1711.11149v2","created_at":"2026-05-17T23:42:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1711.11149","created_at":"2026-05-17T23:42:14Z"},{"alias_kind":"pith_short_12","alias_value":"HYHDGH4IEM35","created_at":"2026-05-18T12:31:21Z"},{"alias_kind":"pith_short_16","alias_value":"HYHDGH4IEM35OILW","created_at":"2026-05-18T12:31:21Z"},{"alias_kind":"pith_short_8","alias_value":"HYHDGH4I","created_at":"2026-05-18T12:31:21Z"}],"graph_snapshots":[{"event_id":"sha256:0c938bb6fe495ed3e93c4d2bf300e04dd153815f5f1f2556daa600ede7a89c66","target":"graph","created_at":"2026-05-17T23:42:14Z","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 $\\Lambda$ be a numerical semigroup, $\\mathcal{C}\\subseteq \\mathbb{A}^n$ the monomial curve singularity associated to $\\Lambda$, and $\\mathcal{T}$ its tangent cone. In this paper we provide a sharp upper bound for the least positive integer in $\\Lambda$ in terms of the codimension and the maximum degree of the equations of $\\mathcal{T}$, when $\\mathcal{T}$ is not a complete intersection. A special case of this result settles a question of J. Herzog and D. Stamate.","authors_text":"Alessio Sammartano","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2017-11-29T23:24:57Z","title":"On the multiplicity of tangent cones of monomial curves"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.11149","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:da33608da1c63bb589eda3267c142cbea1708855ac011ff9e0278f5cec05ce7f","target":"record","created_at":"2026-05-17T23:42:14Z","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":"5f11bd70872eee8ce33bd1c6341162633896ddb802a4b075c632d96d62e25b69","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2017-11-29T23:24:57Z","title_canon_sha256":"5c4cf05b699e15905cbcac86fd4d3b3ffd3f2c786e6746cc64508cea82e2170f"},"schema_version":"1.0","source":{"id":"1711.11149","kind":"arxiv","version":2}},"canonical_sha256":"3e0e331f882337d72176529f144ce3fcfea1c3ce57b88344a109cd9c0ca57a61","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3e0e331f882337d72176529f144ce3fcfea1c3ce57b88344a109cd9c0ca57a61","first_computed_at":"2026-05-17T23:42:14.293830Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:42:14.293830Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"x5dp5RcqfyKcuOP1QjCZN6okP5Ekrny+3YKCqcjlygftNUMXceHblYcyiGCNfXxkezFeYUkCMcrAnrly6N6KCA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:42:14.294572Z","signed_message":"canonical_sha256_bytes"},"source_id":"1711.11149","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:da33608da1c63bb589eda3267c142cbea1708855ac011ff9e0278f5cec05ce7f","sha256:0c938bb6fe495ed3e93c4d2bf300e04dd153815f5f1f2556daa600ede7a89c66"],"state_sha256":"d00f737563080ab5fcbb3d8206ec6dfc9d2f016476decf35fc32cf5a133dacde"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bXqeLbMg5/A50btN26kL1Mi8fscp1WTelUCsNOtMPxfv9Z0UPE6A3gS8VABAUJWERNr/Du/5fVuAn8UWhgs8Bg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T19:22:38.953218Z","bundle_sha256":"d42702fa3d90e435f88b1acfa01ffd23a49cd649a87fcf5619ba4b82135e1a48"}}